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Problemas de Autovalores para EDOs 3

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnRitGOkY9 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

Na parte 1 dessa s\303\251rie de artigos sobre solu\303\247\303\243o de preblemas de autovalores para EDOs, n\303\263s discutimos equa\303\247\303\265es para as quais a solu\303\247\303\243o geral cedeu prontamente autovalores e autofun\303\247\303\265es sem a necessidade de conhecimento detalhado de qualquer uma das fun\303\247\303\265es especiais da matem\303\241tica aplicada. Na parte 2 dessa s\303\251rie, examinamos a solu\303\247\303\243o da equa\303\247\303\243o de Laplace em um cilindro. A separa\303\247\303\243o de vari\303\241veis em coordenadas cil\303\255ndricas leva a um problema singular de autovalor de Sturm-Liouville cuja equa\303\247\303\243o diferencial \303\251 a equa\303\247\303\243o de Bessel. Na parte 3 dessa s\303\251rie, vamos examinar a solu\303\247\303\243o da equa\303\247\303\243o de Laplace em uma esfera. A separa\303\247\303\243o de vari\303\241veis em coordenadas esf\303\251ricas levam a um problema singular de autovalor de Sturm-Liouville no qual a equa\303\247\303\243o diferencial \303\251 a equa\303\247\303\243o de Legendre. Raciocinando a partir de uma solu\303\247\303\243o geral da equa\303\247\303\243o de Legendre para solu\303\247\303\265es limitadas necess\303\241rias para solucionar o problema de autovalor \303\251 um desafio significativamente maior que para o caso paralelo da equa\303\247\303\243o de Bessel. Nossa discuss\303\243o vai destacar as contribui\303\247\303\265es que o Maple pode fazer para esse processo.

Em estado estacion\303\241rio, a temperatura LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em uma esfera satisfaz a equa\303\247\303\243o de LaplaceLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUklbXN1cEdGJDYlLUYsNi1RJiZEZWw7RidGL0YyRjVGN0Y5RjtGPUY/RkEvRkVRLDAuMTExMTExMWVtRictRiM2JC1JI21uR0YkNiRRIjJGJ0YvRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSI9RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjI3Nzc3NzhlbUYnL0ZFRl5vLUZRNiRGVkYvRi8= e a algumas condi\303\247\303\265es no limite da esfera, que s\303\243o descritas em coordenadas esf\303\251ricas por 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 Al\303\251m das condi\303\247\303\265es prescritas na superf\303\255cie LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSJjRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRjY2LVEiLEYnRjJGOS9GPEZQRj1GP0ZBRkNGRS9GSFEmMC4wZW1GJy9GS1EsMC4zMzMzMzMzZW1GJ0Yyas propriedades f\303\255sicas do sistema exige que a sulo\303\247\303\243o seja cont\303\255nua. Essa exig\303\252ncia ser\303\241 a mais importante, e mais dif\303\255cil condi\303\247\303\243o para se impor. Se a temperatura na superf\303\255cie da esfera \303\251 prescrita, dizemos que uma condi\303\247\303\243o de Dirichlet foi imposta. Se a temperatura prescrita na superf\303\255cie \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY2O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj8tSSNtb0dGJDYtUSIsRidGPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRj8=uma fun\303\247\303\243o exclusivamente de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy, a temperatura na esfera ir\303\241 exibir sometria azimutal tal que 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 Alternativamente, se a temperatura prescrita \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRJyYjOTY2O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y/LyUmZmVuY2VHRj4vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NTI7RidGPUY/Rj9GP0ZBRj8=ent\303\243o a temperatura na esfera ir\303\241 exibir assimetria azimutal tal que 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 Se a superf\303\255cie da esfera \303\251 isolada tal que o fluxo total de calor atrav\303\251s da superf\303\255cie \303\251 zero, dizemos que uma condi\303\247\303\243o homog\303\252nea de Neumann foi imposta. O fluxo atrav\303\251s da superf\303\255cie \303\251 a derivada normal dada por 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 avaliada em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSJjRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRjY2LVEiLEYnRjJGOS9GPEZQRj1GP0ZBRkNGRS9GSFEmMC4wZW1GJy9GS1EsMC4zMzMzMzMzZW1GJ0Yyonde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 o raio da esfera. O fluxo total seria a integral da superf\303\255cie dessa derivada. Entretanto, se o fluxo total atrav\303\251s da superf\303\255cie de uma esfera homog\303\252nea \303\251 zero, a temperatura de estado estacion\303\241rio na esfera ser\303\241 constante.

A partir de nossa afirma\303\247\303\243o do problema acima, nossa defini\303\247\303\243o de coordenadas esf\303\251ricas pode ser inferida. Entretanto, por causa da exist\303\252ncia de dois usos diferentes na literatura, iremos explicitamente definir nosso sistema de acordo com a nota\303\247\303\243o na maioria dos artigos matem\303\241ticos. Em tais artigos, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy \303\251 a dist\303\242ncia da origem; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMg== medido a partir do eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= positivo e em torno do eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, pertence ao intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHRjhGL0YyLUYsNiRRIjJGJ0YvLUYzNi1RIn5GJ0YvRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGVy1GSzYlUScmIzk2MDtGJ0ZORi9GLw==; e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMg==medido no sentido descendente do a partir do eixo positivo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, pertence ao intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHRjhGL0YyLUZLNiVRJyYjOTYwO0YnRk5GLy1GMzYtUSIuRidGL0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRldGLw== As equa\303\247\303\265es conectando essas coordenadas esf\303\251ricas com coordenadas Cartesianas aparecem \303\240 esquerda na Tabela 1. Coordenads esf\303\251ricas em artigos para f\303\255sica, engenharia, e ci\303\252ncias aplicadas tendem a intercambiar os nomes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYy As equa\303\247\303\265es conectando essas coordenadas esf\303\251ricas com coordenadas Cartesianas aparecem \303\240 direita na Tabela 1. Artigos Matem\303\241ticos \303\202ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy medido abaixo do eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= Artigos de Ci\303\252ncia \303\202ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy medido abaixo do eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYlUSJ6RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJiZyaG87RicvRjVGQkY+LUY7Ni1RIn5GJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRJjAuMGVtRicvRlNGZm4tRiw2JVEkY29zRidGV0Y+LUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEnJiM5NTI7RidGV0Y+Rj5GPkY+RitGPg== Tabela 1 Coordenadas esf\303\251ricas como definidas em artigos matem\303\241ticos(esquerda) e em artigos de ci\303\252ncia (direita) Finalmente, note que no pacote VectorCalculus do Maple, comandos que usam coordenadas esf\303\251ricas assumem que a coordenada do "meio" no trio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEidkYnRi9GMkY1LUYsNiVRIndGJ0YvRjJGOQ== \303\251 o \303\242ngulo medido para baixo a partir do eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Infelizmente, em um n\303\272mero comandos de constru\303\247\303\243o de gr\303\241ficos no pacote plots, essa conven\303\247\303\243o n\303\243o \303\251 respeitada. O Maple est\303\241 atualmente lutando com esse dilema, especialmente esse caso, dado seu comprometimento com a retrocompatibilidade. Estabelecemos o sistema coordenado ambiente via comando 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

Em uma esfera, a temperatura em estado estacion\303\241rio 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 satisfaz a equa\303\247\303\243o de Laplace 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 Essa equa\303\247\303\243o \303\251 dada no Maple como 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNMRUdGKC8sLCooIiIjIiIiSSRyaG9HRighIiItSSVkaWZmR0YmNiQtSSJ1R0YoNiVGM0kpJnZhcnBoaTtHRihJJnRoZXRhR0YoRjNGMkYyLUY2NiRGOC1JIiRHRiY2JEYzRjFGMioqKUYzRjFGNC1JJHNpbkdGJTYjRjtGNC1JJGNvc0dGJUZGRjItRjY2JEY4RjtGMkYyKiZGQ0Y0LUY2NiRGOC1GQDYkRjtGMUYyRjIqKEZDRjQpRkRGMUY0LUY2NiRGOC1GQDYkRjxGMUYyRjIiIiE3Iy8sLEYwRjItRjY2JEY1RjNGMkZCRjIqJkZDRjQtRjY2JEZJRjtGMkYyKihGQ0Y0RlFGNC1GNjYkLUY2NiRGOEY8RjxGMkYyRlY=

O Maple pode determinar se a equa\303\247\303\243o derivada parcial possui vari\303\241veis separ\303\241veis: 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

IiIh

O resultado "0" indica que a equa\303\247\303\243o \303\251 de fato separ\303\241vel porque as condi\303\247\303\265es de separa\303\247\303\243o s\303\243o identicamente satisfeitas.

Sob a suposi\303\247\303\243o de que temperaturas de estado estacion\303\241rio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= s\303\243o sim\303\251tricas em rela\303\247\303\243o ao eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, a depend\303\252ncia do \303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy pode ser dispensada. Portanto, 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e uma separa\303\247\303\243o de vari\303\241veis gerada pelo Maple \303\251 obtida com 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSScmd2hlcmVHRig2JC8tSSJ1R0YoNiRJJHJob0dGKEkpJnZhcnBoaTtHRigqJi1JJF9GMUdGKDYjRjMiIiItSSRfRjJHRig2I0Y0Rjk3IzwkLy1JJWRpZmZHRiY2JEY2LUkiJEdGJjYkRjMiIiMsJiooKUYzRkYhIiJGNkY5JkkjX2NHRiU2I0Y5RjlGOSooRkZGOUYzRkotRkE2JEY2RjNGOUZKLy1GQTYkRjotRkQ2JEY0RkYsJiomRjpGOUZLRjlGSiooLUkkc2luR0YlRjxGSi1JJGNvc0dGJUY8RjktRkE2JEY6RjRGOUZKNyMtSSxQREVTb2xTdHJ1Y0dGJjYkRi83IzwkLy1GQTYkRmduRjRGVi8tRkE2JEZPRjNGRw==

A equa\303\247\303\243o 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 mostra uma solu\303\247\303\243o da separa\303\247\303\243o de vari\303\241veis da forma 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJVR0YoKiYtSSRSaG9HRig2I0kkcmhvR0YoIiIiLUkkUGhpR0YoNiNJKSZ2YXJwaGk7R0YoRjM3I0Yu

exists, and provides the ordinary differential equations the functions LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5Mjk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTYxO0YnRi9GMkYyRjJGMg== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5MzQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY2O0YnRi9GMkYyRjJGMg== must satisfy. We now proceed to obtain these same results from first principles. Sob a suposi\303\247\303\243o de separa\303\247\303\243o, a equa\303\247\303\243o de Laplace assume a forma simples 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiIiLywqKioiIiNGMEkkcmhvR0YoRjAtSSRSaG9HRig2I0Y1ISIiLUklZGlmZkdGJjYkRjZGNUYwRjAqKClGNUY0RjBGNkY5LUY7NiRGNi1JIiRHRiY2JEY1RjRGMEYwKiotSSRQaGlHRig2I0kpJnZhcnBoaTtHRihGOS1JJHNpbkdGJUZHRjktSSRjb3NHRiVGR0YwLUY7NiRGRUZIRjBGMComRkVGOS1GOzYkRkUtRkI2JEZIRjRGMEYwIiIhNyMvLCpGM0YwKihGPkYwRjZGOS1GOzYkRjpGNUYwRjBGREYwKiZGRUY5LUY7NiRGTUZIRjBGMEZU

Movendo todos os termos em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy para a direita, ent\303\243o temos 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiIjLywmKipGMCIiIkkkcmhvR0YoRjQtSSRSaG9HRig2I0Y1ISIiLUklZGlmZkdGJjYkRjZGNUY0RjQqKClGNUYwRjRGNkY5LUY7NiRGNi1JIiRHRiY2JEY1RjBGNEY0LCYqKi1JJFBoaUdGKDYjSSkmdmFycGhpO0dGKEY5LUkkc2luR0YlRkhGOS1JJGNvc0dGJUZIRjQtRjs2JEZGRklGNEY5KiZGRkY5LUY7NiRGRi1GQjYkRklGMEY0Rjk3Iy8sJkYzRjQqKEY+RjRGNkY5LUY7NiRGOkY1RjRGNCwmRkVGOSomRkZGOS1GOzYkRk5GSUY0Rjk=

Introdu\303\247\303\243o da constante de separa\303\247\303\243o de Bernoulli LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy leva ent\303\243o \303\240s equa\303\247\303\265es diferenciais ordin\303\241rias LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1JJW1zdWJHRiQ2JS1GLDYlUSJxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIzRicvRjtRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RidGQy8lJmZlbmNlR0ZHLyUqc2VwYXJhdG9yR0ZHLyUpc3RyZXRjaHlHRkcvJSpzeW1tZXRyaWNHRkcvJShsYXJnZW9wR0ZHLyUubW92YWJsZWxpbWl0c0dGRy8lJ2FjY2VudEdGRy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmluLUYjNictRiw2JVEkbGhzRidGN0Y6LUZMNjFRMCZBcHBseUZ1bmN0aW9uO0YnLyUnZmFtaWx5R1Emc2VyaWZGJy8lJWJvbGRHRjlGRS9GO1ElYm9sZEYnLyUrZm9udHdlaWdodEdGam9GT0ZRRlNGVUZXRllGZW4vRmhuUSYwLjBlbUYnL0Zbb0ZecC1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYyNiVGNC1GIzYlLUZANiRRIjJGJ0ZDRkVGQ0ZIRkVGQ0ZDRkVGQy1GTDYtUSI9RidGQ0ZPRlFGU0ZVRldGWUZlbkZnbkZqbi1GLDYlUScmIzk1NTtGJy9GOEZHRkNGRUZDRitGRUZD 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiIkLywmKioiIiMiIiJJJHJob0dGKEY1LUkkUmhvR0YoNiNGNiEiIi1JJWRpZmZHRiY2JEY3RjZGNUY1KigpRjZGNEY1RjdGOi1GPDYkRjctSSIkR0YmNiRGNkY0RjVGNUknbGFtYmRhR0YoNyMvLCZGM0Y1KihGP0Y1RjdGOi1GPDYkRjtGNkY1RjVGRQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiIlLywmKiotSSRQaGlHRig2I0kpJnZhcnBoaTtHRighIiItSSRzaW5HRiVGNkY4LUkkY29zR0YlRjYiIiItSSVkaWZmR0YmNiRGNEY3Rj1GOComRjRGOC1GPzYkRjQtSSIkR0YmNiRGNyIiI0Y9RjhJJ2xhbWJkYUdGKDcjLywmRjNGOComRjRGOC1GPzYkRj5GN0Y9RjhGSA==

Estamos primeiramente interessados na segunda dessas equa\303\247\303\265es - le ir\303\241 se tornar a equa\303\247\303\243o de Legendre ap\303\263s uma leve rearruma\303\247\303\243o e mudan\303\247a de vari\303\241veis. Primeiro, escrevemos a equa\303\247\303\243o na forma 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiImLyIiISwoSSdsYW1iZGFHRigiIiIqKi1JJFBoaUdGKDYjSSkmdmFycGhpO0dGKCEiIi1JJHNpbkdGJUY5RjstSSRjb3NHRiVGOUY1LUklZGlmZkdGJjYkRjdGOkY1RjUqJkY3RjstRkE2JEY3LUkiJEdGJjYkRjoiIiNGNUY1NyMvRjIsKEY0RjVGNkY1KiZGN0Y7LUZBNiRGQEY6RjVGNQ==

e ent\303\243o 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiInLyIiISwoKigtSSRQaGlHRig2I0kpJnZhcnBoaTtHRigiIiItSSRzaW5HRiVGN0Y5SSdsYW1iZGFHRihGOUY5KiYtSSRjb3NHRiVGN0Y5LUklZGlmZkdGJjYkRjVGOEY5RjkqJkY6RjktRkE2JEY1LUkiJEdGJjYkRjgiIiNGOUY5NyMvRjIsKEY0RjlGPUY5KiZGOkY5LUZBNiRGQEY4RjlGOQ==

Agora, fazemos a mudan\303\247a de vari\303\241veis 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com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5MzQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY2O0YnRi9GMkYyRjItRiw2I1EhRidGMg== se tornando 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 Isso \303\251 feito no Maple com 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiIoLyIiISomLDAqJi1JInlHRig2I0kieEdGKCIiIkknbGFtYmRhR0YoRjpGOiooRjZGOkY7RjopRjkiIiNGOiEiIiooRj5GOi1JJWRpZmZHRiY2JEY2RjlGOkY5RjpGPyooRj5GOilGOSIiJEY6RkFGOkY6LUZCNiRGNi1JIiRHRiY2JEY5Rj5GOiooRj5GOkZHRjpGPUY6Rj8qJkZHRjopRjkiIiVGOkY6RjopLCZGOkY6KiRGPUY6Rj8jRjpGPkY/NyMvRjIqJiwwRjVGOkY8Rj9GQEY/RkRGOi1GQjYkRkFGOUY6KihGPkY6RlhGOkY9RjpGPyomRlhGOkZORjpGOkY6RlBGPw==

Mais simplificadamente, temos 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiIpLyIiISwoKiYsJiIiIkY2KiQpSSJ4R0YoIiIjRjYhIiJGNi1JJWRpZmZHRiY2JC1JInlHRig2I0Y5LUkiJEdGJjYkRjlGOkY2RjYqKEY6RjYtRj02JEY/RjlGNkY5RjZGOyomRj9GNkknbGFtYmRhR0YoRjZGNjcjL0YyLCgqJkY1RjYtRj02JEZGRjlGNkY2RkVGO0ZIRjY=

que \303\251 a forma padr\303\243o da equa\303\247\303\243o de Legendre, a forma auto-adjunta do qual poderia ser 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

O problema de autovalor que embute a equa\303\247\303\243o de Legendre \303\251 singular. As condi\303\247\303\265es limite s\303\243o simplesmente que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== deve ser cont\303\255nua no intervalo 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 A passagem da solu\303\247\303\243o geral 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

Ly1JInlHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JKkxlZ2VuZHJlUEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLCYqJiNGKyIiI0YrKSwmKiYiIiVGK0knbGFtYmRhR0YlRitGK0YrRitGNEYrRitGNCEiIkYnRitGKyomSSRfQzJHRiVGKy1JKkxlZ2VuZHJlUUdGLkYxRitGKw==

para as autofun\303\247\303\265es \303\251 surpreendentemente mais dif\303\255cil do que era para a equa\303\247\303\243o de Bessel. Porque estamos no modo prorrogado de composi\303\247\303\243o, as fun\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== s\303\243o mostradas como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImFGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGMkY1Rj1GPUY9 e 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respectivamente. (Est\303\241vamos no modo prorrogado de composi\303\247\303\243o durante nossa discuss\303\243o anterior da equa\303\247\303\243o de Bessel, o Maple deveria ter exibido LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoQmVzc2VsSkYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJhRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictSSNtb0dGJDYtUSIsRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInhGJ0Y9Rj9GMkYyRjI= como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImFGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGMkY1Rj1GPS1JI21vR0YkNi1RIi5GJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZQLyUpc3RyZXRjaHlHRlAvJSpzeW1tZXRyaWNHRlAvJShsYXJnZW9wR0ZQLyUubW92YWJsZWxpbWl0c0dGUC8lJ2FjY2VudEdGUC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmluRj0=) Quando solucionamos a equa\303\247\303\243o de Laplace no cilindro, foi relativamente f\303\241cil restringir a solu\303\247\303\243o geral para somente 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, a fun\303\247\303\243o de Bessel limitada no intervalo 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 determinar os autovalores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYvNiVRImtGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNQ== dos zeros de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHRj0tSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGMkY1Rj5GPi1JI21vR0YkNi1RIi5GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZQLyUpc3RyZXRjaHlHRlAvJSpzeW1tZXRyaWNHRlAvJShsYXJnZW9wR0ZQLyUubW92YWJsZWxpbWl0c0dGUC8lJ2FjY2VudEdGUC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmluRj4= Come\303\247amos o processo descartando a fun\303\247\303\243o de Bessel de segundo tipo porque poder\303\255amos dizer a partir de um gr\303\241fico que tais fun\303\247\303\265es eram ilimitadas na horigem. Tentaremos eliminar a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== em um modo similar, mas iremos achar o preoceso mais dif\303\255cil que era para a fun\303\247\303\243o de Bessel. Por exemplo, considere 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

LCwqJiMiIiIiIiVGJS1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkieEdGLEYlRiVGJUYlISIiKiZGJEYlLUYoNiMsJkYlRjBGL0YlRiVGJSooIyIiJEYmRiUpRi8iIiNGJUYnRiVGJSooRjZGJUY4RiVGMkYlRjAqJiNGN0Y5RiVGL0YlRjA=

do qual \303\251 claro que a fun\303\247\303\243o \303\251 ilimitada nos pontos finais LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSUmcG07RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORlMtSSNtbkdGJDYkUSIxRidGOUY5 por causa dos logaritmos. Mas isso \303\251 \303\263bvio para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=, um inteiro. \303\211 um pouco mais dif\303\255cil adivinhar o comportamente dos pontos finais para valores gerais de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Por exemplo, podemos calcular os valores 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

LCYkIiIiSSlpbmZpbml0eUclKnByb3RlY3RlZEdGJComRiNGJF4jRiRGJEYk

LCYkIiIiSSlpbmZpbml0eUclKnByb3RlY3RlZEdGJComRiNGJF4jRiRGJEYk

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Figura 1 Partes real e imagin\303\241ria de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== para 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sugerindo que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== \303\251 ilimitada em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZOLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZKRkZGLw== A partir da Figura 1(a) especialmente, conclu\303\255mos que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqTGVnZW5kcmVRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSNtbkdGJDYkUSIxRidGMkYyRjItRiw2I1EhRidGMg== \303\251 ilimitada para valores gerais de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Na base dessa conclus\303\243o, estabelecemos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkX0MyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== para zero na solu\303\247\303\243o geral da equa\303\247\303\243o de Legendre, e mudamos nossa aten\303\247\303\243o para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGQUYya fun\303\247\303\243o de Legendre de primeiro tipo. Primeiro mostramos que pra valores gerais (reais) de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGOQ==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 \303\251 ilimitada. C\303\241lculos simb\303\263licos incluem 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

LCYkIiIiSSlpbmZpbml0eUclKnByb3RlY3RlZEdGJComRiNGJF4jRiRGJEYk

Para ilustrar esse comportamento para m\303\255ltiplos valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, definimos a seguinte fun\303\247\303\243o por partes. 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoLUkqUElFQ0VXSVNFR0YlNiQ3JCIiIzIiJSs1LUkkYWJzR0YmNiMtSSpMZWdlbmRyZVBHRiU2JEkiYUdGKCEiIjckRjhJKm90aGVyd2lzZUdGKDcjLUkqcGllY2V3aXNlR0YmNiVGM0YyRjg=

Se 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 grande, ent\303\243o um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImFGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== ir\303\241 mostrar um ponto em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjJGJ0Y+Rj5GPkY+ para esse valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiUtSSNtaUdGJDYlUSpMZWdlbmRyZVBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiQtRiM2Jy1GMTYlUSJhRicvRjVRJXRydWVGJy9GOFEnaXRhbGljRictSSNtb0dGJDYtUSIsRidGNy8lJmZlbmNlR0Y2LyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRjYvJShsYXJnZW9wR0Y2LyUubW92YWJsZWxpbWl0c0dGNi8lJ2FjY2VudEdGNi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZGNi1RKiZ1bWludXMwO0YnRjdGSS9GTEY2Rk1GT0ZRRlNGVS9GWFEsMC4yMjIyMjIyZW1GJy9GZW5GXG8tSSNtbkdGJDYkUSIxRidGN0Y3RjdGN0Y3LyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRmRvLUYxNiNRIUYnRjc= \303\251 "n\303\243o grande" ent\303\243o um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImFGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== mostrar\303\241 o valor de 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 Podemos controlar a avalia\303\247\303\243o dos pontos para um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImFGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== se definirmos a vari\303\241vel aleat\303\263ria uniforme LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= via 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 ent\303\243o criar uma amostra uniforme por\303\251m aleat\303\263ria de valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= que incluem os inteiros no intervalo 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. 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 O gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImFGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== na Figura 2 mostra que virtualmente todas as avalia\303\247\303\265es de 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s\303\243o grandes em magnitude. 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

Figura 2 Gr\303\241fico estilizado de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRkI2LVEqJnVtaW51czA7RidGMkZFL0ZIRjFGSUZLRk1GT0ZRL0ZUUSwwLjIyMjIyMjJlbUYnL0ZXRmhuLUkjbW5HRiQ2JFEiMUYnRjJGMkYyRjI= para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIzRidGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZOLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZKRkZGLw== Entretanto, ele tamb\303\251m sugere que 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= inteiro. Para n\303\243o inteiro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImFGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== \303\251 ilimitado tal que as solu\303\247\303\265es limitadas da equa\303\247\303\243o de Legendre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiOEYnL0Y2USdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZARj4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvIiIhLCgqJiwmIiIiRjEqJClJInhHRigiIiNGMSEiIkYxLUklZGlmZkdGJjYkLUkieUdGKDYjRjQtSSIkR0YmNiRGNEY1RjFGMSooRjVGMS1GODYkRjpGNEYxRjRGMUY2KiZGOkYxSSdsYW1iZGFHRihGMUYxNyMvRi0sKComRjBGMS1GODYkRkFGNEYxRjFGQEY2RkNGMQ==

ser\303\243o as autofun\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImtGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== com 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

L0kia0c2IiwmKiYjIiIiIiIjRigpLCYqJiIiJUYoSSdsYW1iZGFHRiRGKEYoRihGKEYnRihGKEYnISIi

um inteiro. Portanto, os autovalores ser\303\243o 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

LCYqJClJImtHNiIiIiMiIiJGKEYlRig=

isso \303\251, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYvNiVRImtGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSI9RidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlhGOi1GRTYtUSJ+RidGNUZIRkpGTEZORlBGUkZUL0ZXUSYwLjBlbUYnL0ZaRmluLUkobWZlbmNlZEdGJDYkLUYjNiZGOi1GRTYtUSIrRidGNUZIRkpGTEZORlBGUkZUL0ZXUSwwLjIyMjIyMjJlbUYnL0ZaRmRvLUkjbW5HRiQ2JFEiMUYnRjVGNUY1LUZFNi1RIixGJ0Y1RkgvRktGPkZMRk5GUEZSRlRGaG4vRlpRLDAuMzMzMzMzM2VtRidGOkZELUZnbzYkRkNGNUZqb0Zmb0Zqby1GRTYtUSkmaGVsbGlwO0YnRjVGSEZKRkxGTkZQRlJGVC9GV1EsMC4xNjY2NjY3ZW1GJy9GWkZmcC1GRTYtUSIuRidGNUZIRkpGTEZORlBGUkZURmhuRmpuRjU= As primeiras autofun\303\247\303\265es s\303\243o 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQMEdGKCIiIjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQMUdGKEkieEdGKDcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQMkdGKCwmIyIiIiIiIyEiIiomIyIiJEYxRjApSSJ4R0YoRjFGMEYwNyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQM0dGKCwmKiYjIiImIiIjIiIiKUkieEdGKCIiJEYzRjMqJiNGNkYyRjNGNUYzISIiNyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNQNEdGKCwoIyIiJCIiKSIiIiomIyIjTkYxRjIpSSJ4R0YoIiIlRjJGMiomIyIjOkY4RjIpRjciIiNGMiEiIjcjRi4=

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que s\303\243o os polin\303\264mios de Legendre 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normalizados do modo que 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 Esses polin\303\264mios possuem seus gr\303\241ficos na Figura 3. 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Figura 3 Os polin\303\264mios de Legendre 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 Que a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== reduza para o polin\303\264mio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImtGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGMkY1Rj1GPUY9 for 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 ser visto a partir dos seguintes c\303\241lculos. Para n\303\243o inteiro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, primeiros obtemos a expans\303\243o da s\303\251rie de pot\303\252ncia formal LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== via 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

ent\303\243o extra\303\255mos o termo geral na primeira s\303\251rie com 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O s\303\255mbolo pochhammer 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 ou "aumento fatorial" pra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= complexo generaliza para 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy complexo. Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um inteiro n\303\243o positivo, ent\303\243o 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 Fazendo essa transforma\303\247\303\243o e estabelecendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk= no termo geral da primeira s\303\251rie de para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== d\303\241 o coeficiente geral 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Para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= grande esse coeficiente \303\251 assint\303\263tico a 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

LCQqKiMiIiIiIiNGJS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiZJI1BpR0YqRiVJImFHRixGJUYlSSJrR0YsISIiRi9GMkYy

sugerindo que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSNtbkdGJDYkUSIxRidGMkYyRjItRiw2I1EhRidGMg== \303\251 ilimitado desde que a s\303\251rie considerada se comporte como a s\303\251rie harm\303\264nica em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=. Podemos confirmar esse comportamento comparando o coeficiente geral com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGMi8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRC8lKWJldmVsbGVkR1EmZmFsc2VGJ0Yy para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= grande. No limite encontramos a raz\303\243o tendendo a 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

LCQqMCIiIyIiIkkjUGlHJSpwcm90ZWN0ZWRHRiUtSSZHQU1NQUc2JEYnSShfc3lzbGliRzYiNiMsJiNGJUYkRiUqJkYvRiVJImFHRixGJSEiIkYyLUYpNiMsJEYwRiVGMkYxRjItRik2IywkRjBGMkYyLUYpNiMsJkYwRiVGL0YlRjJGJQ==

que \303\251 finito para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= n\303\243o inteiro. Para ver que para inteiro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= a s\303\251rie para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjJGMg== reduz-se para um polin\303\264mio, examine a f\303\263rmula de recurs\303\243o para seus coeficientes. Isso \303\251 mais eficientemente obtido no Maple via 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

Ly1JInVHNiI2IywmSSJrR0YlIiIiIiIjRikqKiwoSSdsYW1iZGFHRiUhIiJGKEYpKiQpRihGKkYpRilGKS1GJDYjRihGKSwmRihGKUYpRilGLkYnRi4=

Do qual se torna claro que 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 quando 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 Portanto, 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 Por esse motivo, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRImtGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRj1GP0YyRjItRiw2I1EhRidGMg== \303\251 um polin\303\264mio de grau LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSJrRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRjY2LVEifkYnRjJGOUY7Rj1GP0ZBRkNGRS9GSFEmMC4wZW1GJy9GS0ZXLUkobWZlbmNlZEdGJDYkLUYjNiZGTC1GNjYtUSIrRidGMkY5RjtGPUY/RkFGQ0ZFL0ZIUSwwLjIyMjIyMjJlbUYnL0ZLRlxvLUkjbW5HRiQ2JFEiMUYnRjJGMkYyLUY2Ni1RIi5GJ0YyRjlGO0Y9Rj9GQUZDRkVGVkZYRjI=

A prova cl\303\241ssica de que a ortogonalidade das autofun\303\247\303\265es da equa\303\247\303\243o de Legendre \303\251 baseada na integra\303\247\303\243o por partes. A forma auto-adjunta da equa\303\247\303\243o, nomeada, 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 \303\251 escrita uma vez por uma autofun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== e outra por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIuRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURj0= A primeira equa\303\247\303\243o \303\251 multiplicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0Y9e a segunda, por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==, e a diferen\303\247a dos dois produtos \303\251 integrada sobre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZOLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZKRkZGLw==. A integra\303\247\303\243o por partes \303\251 aplicada aos termos contendo derivadas, que desaparecem como podemos ver a partir do esbo\303\247o abaixo. As integrais dos termos contendo as derivadas pode ser escrito como 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM2LUkkSW50R0YlNiQqJi1JInVHRig2I0kieEdGKCIiIi1JJURpZmZHRiU2JComLCZGOUY5KiQpRjgiIiNGOSEiIkY5LUklZGlmZkdGJjYkLUkidkdGKEY3RjhGOUY4RjkvRjg7RkJGOTcjRjE=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM3LUkkSW50R0YlNiQqJi1JInZHRig2I0kieEdGKCIiIi1JJURpZmZHRiU2JComLCZGOUY5KiQpRjgiIiNGOSEiIkY5LUklZGlmZkdGJjYkLUkidUdGKEY3RjhGOUY4RjkvRjg7RkJGOTcjRjE=

A integra\303\247\303\243o por partes e a subtra\303\247\303\243o ent\303\243o levam a 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

IiIh

O que sobra \303\251 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 Se os autovalores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYvNiVRInVGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYvNiVRInZGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNQ== s\303\243o diferentes, ent\303\243o 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o que implica a ortogonalidade de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Desse modo, 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 for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJrRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRidGOQ==como podemos ver de 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 via a matriz de avalia\303\247\303\265es abaixo. 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqLysteCItSSdNQVRSSVhHRig2IzcoNygiIiMiIiFGNkY2RjZGNjcoRjYjRjUiIiRGNkY2RjZGNjcoRjZGNiNGNSIiJkY2RjZGNjcoRjZGNkY2I0Y1IiIoRjZGNjcoRjZGNkY2RjYjRjUiIipGNjcoRjZGNkY2RjZGNiNGNSIjNkknTWF0cml4R0YlNyMtRkY2Iy9JJCVpZEdGKEYv

Dessa matriz podemos inferir tamb\303\251m que 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, um resultado que o Maple n\303\243o pode mostrar em geral, como vemos de 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

LUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJCktSSpMZWdlbmRyZVBHRiQ2JEkia0dGJ0kieEdGJyIiIyIiIi9GLzshIiJGMQ==

Uma fun\303\247\303\243o integr\303\241vel 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pode ser representada pela s\303\251rie de Fourier-Legendre 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onde 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 Os coeficientes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImtGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0Y6LUZDNi1RIj1GJ0Y9RkYvRkpGSEZLRk1GT0ZRRlMvRlZRLDAuMjc3Nzc3OGVtRicvRllGam4tSSNtbkdGJDYkRkFGPUZCLUZdbzYkUSIxRidGPUZCLUZDNi1RKSZoZWxsaXA7RidGPUZGRmhuRktGTUZPRlFGUy9GVlEsMC4xNjY2NjY3ZW1GJy9GWUZmb0ZCLUZdbzYkUSI1RidGPUZCRj0=para a s\303\251rie de Fourier-Legendre da fun\303\247\303\243o 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s\303\243o 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LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYUdGKDYjIiIlLCQqJiMiIioiJGMjIiIiSSNQaUdGJkY2ISIiNyNGMQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYUdGKDYjIiImIiIhNyNGMQ==

Uma soma parcial da s\303\251rie de Fourier-Legendre \303\251 ela mesma dada por 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRGTGZHRigsKComIyIiIiIiJUYxSSNQaUdGJkYxRjEqKCMiIiYiI0tGMUYzRjEtSSpMZWdlbmRyZVBHRiU2JCIiI0kieEdGKEYxISIiKigjIiIqIiRjI0YxRjNGMS1GOTYkRjJGPEYxRj03I0Yu

ou melhor ainda, por 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

LCgqJiMiJFgnIiVbPyIiIkkjUGlHJSpwcm90ZWN0ZWRHRidGJyooIyIkMCIiJUM1RidGKEYnKUkieEc2IiIiI0YnISIiKigjIiQ6JEYmRidGKEYnKUYvIiIlRidGMg==

A Figura 4 compara gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== e a soma parcial de suas s\303\251ries de Fourier-Legendre. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjFRMCZBcHBseUZ1bmN0aW9uO0YnLyUnZmFtaWx5R1Emc2VyaWZGJy8lJWJvbGRHRjgvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOlElYm9sZEYnLyUrZm9udHdlaWdodEdGSS8lJmZlbmNlR0ZHLyUqc2VwYXJhdG9yR0ZHLyUpc3RyZXRjaHlHRkcvJSpzeW1tZXRyaWNHRkcvJShsYXJnZW9wR0ZHLyUubW92YWJsZWxpbWl0c0dGRy8lJ2FjY2VudEdGRy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmZuLUkobWZlbmNlZEdGJDYkLUYjNi4tRmpuNiYtRiM2Jy1GLDYlUSJmRidGNkY5LUY9Ni1RIixGJy9GOlEnbm9ybWFsRidGTC9GT0Y4RlBGUkZURlZGWEZaL0ZoblEsMC4zMzMzMzMzZW1GJy1GLDYlUSRGTGZGJ0Y2RjlGRUZob0Zoby8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zlby1GIzYoLUYsNiVRInhGJ0Y2RjktRj02LVEiPUYnRmhvRkxGTkZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZfcS1GIzYoRistRiM2Ji1GPTYtUSomdW1pbnVzMDtGJ0Zob0ZMRk5GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GaXEtSSNtbkdGJDYkUSIxRidGaG9GRUZoby1GPTYtUSMuLkYnRmhvRkxGTkZQRlJGVEZWRlhGaHFGZ25GW3JGRUZob0YrRkVGaG9GZW8tRiM2Jy1GLDYlUSZjb2xvckYnRjZGOUZbcS1Gam42Ji1GIzYnLUYsNiVRJmJsYWNrRidGNkY5RmVvLUYsNiVRJHJlZEYnRjZGOUZFRmhvRmhvRmBwRmNwRkVGaG9GZW8tRiM2Jy1GLDYlUSp0aGlja25lc3NGJ0Y2RjlGW3EtRmpuNiYtRiM2Jy1GXHI2JFEiNUYnRmhvRmVvLUZccjYkUSIyRidGaG9GRUZob0Zob0ZgcEZjcEZFRmhvRmVvLUYjNictRiw2JVEoc2NhbGluZ0YnRjZGOUZbcS1GLDYlUSxjb25zdHJhaW5lZEYnRjZGOUZFRmhvRitGRUZob0Zob0ZFRmhvRitGRUZob0YrRkVGaG8=

LSUlUExPVEc2KC0lJ0NVUlZFU0c2JTdfbzckJCEjNSEiIiQiIiEhIiI3JCQhMW47SGROdnMqKiEjOyQiMFY7c2wqKm9QKCEjOzckJCExTUxlOXJdWCoqISM7JCIydmQ3K0tSRC8iISM8NyQkITEsXSg9bmcjPSoqISM7JCIyJSpcI0d1QShmRiIhIzw3JCQhMW5tO0hVLCIqKSohIzskIjJpWFAjNHlOczkhIzw3JCQhLXZWOF9PKSohIzckIjJZJHB5Jyozeis9ISM8NyQkITFNTExlJUc/eSohIzskIjJFS0owODtsMiMhIzw3JCQhLHZvVUluKiEjNiQiMjIlUVlKcj1PRCEjPDckJCExbm1tO3AwayYqISM7JCIyWEcmZVtOVD9IISM8NyQkIS12VjVTdSQqISM3JCIxJ0drcSRmWSJbJCEjOzckJCExTEwkMzxYWj0qISM7JCIxKlIiM2Q7IVsmUiEjOzckJCExKioqXGlJZDkoKikhIzskIjEncEMqPXBNPFchIzs3JCQhMW5tbVQlcCJlKCkhIzskIjJYKHkheUhNayNbISM8NyQkITFtbW0iNG0oRyQpISM7JCIxKkgtQz4oZU1iISM7NyQkITFNTCQzaS45IXohIzskIjE4KipILSVmI0hoISM7NyQkITFubTsvUj0wdiEjOyQiMEY7YmomXDNtISM6NyQkISx2TEBcNCghIzYkIjBjbWZhTHIvKCEjOjckJCExbm07L3NpcW0hIzskIjFkbmo8YyxddSEjOzckJCEsdnkkcFppISM2JCIxUjclb1EkNDN5ISM7NyQkITFMTEwkeWFFImUhIzskIjElUWRdIilScjgpISM7NyQkITFubW0iPnMlSGEhIzskIjEnUjw2Qm93UikhIzs3JCQhMi8rKytOKjQpKlwhIzwkIjFaMWUrNk5oJykhIzs3JCQhKkRiXGMlISIqJCIxOl8rIjNkcyopKSEjOzckJCEqbFN2OSUhIiokIjEoR0UzXU4kKjQqISM7NyQkITFubTsvIylbb1AhIzskIjF5LSQ9elpGRSohIzs3JCQhMk9MTEw9ZXhKJCEjPCQiMHQjPilmI2VMJSohIzo3JCQhMU1MTEwyJGYkSCEjOyQiMVY3PUhcSWYmKiEjOzckJCEyMCsrdmp1PFwjISM8JCIxajU2PiV5WG8qISM7NyQkITJWTExMQkAnKTQjISM8JCIxOT4nPiEqNHR4KiEjOzckJCEyJyoqKipcUCdwc20iISM8JCIxRmg+SzUuZykqISM7NyQkISxEIjRfYzchIzYkIjFwQmkib1YyIyoqISM7NyQkITFKTEwkM3gleiMpISM8JCIxIm8lMyo9bWMnKiohIzs3JCQhMU1MTDNzJFFNJSEjPCQiMWR1XCUzaDAqKiohIzs3JCQhMV5vbW07enIpKiEjPiQiMXhfUUZeKioqKioqISM7NyQkIjE8TExlenc1ViEjPCQiMVIySz5WcSEqKiohIzs3JCQiMCoqKipcUFEjXCIpISM7JCIxXzRSVydSbicqKiEjOzckJCIyQkxMJGUiKltINyEjPCQiMSdRIXAyKzhDKiohIzs3JCQiMiQqKioqKioqcHZ4bCIhIzwkIjFzOjEocEo7JykqISM7NyQkIjEpKioqKlxfcW4yIyEjOyQiMUdLTl9XKD55KiEjOzckJCIyJSkqKipcaSZwQFsjISM8JCIxV3YkNG1XcW8qISM7NyQkIjEpKioqKlwyJ0hLSCEjOyQiMVx0a3kvVWcmKiEjOzckJCIxbG1tbVp2T0whIzskIjFjIWV6MCEpb1UqISM7NyQkIjInKioqKioqXDJnb1AhIzwkIjFEISpcLT9xaSMqISM7NyQkIjJDTExlUjwqZlQhIzwkIjBMajcjUm8kNCohIzo3JCQiMigqKioqKipcKUh4ZSUhIzwkIjEiZiVlWF5gJikpKSEjOzckJCIyWW1tIkghby0qXCEjPCQiMURJbjJiJ2VtKSEjOzckJCIxKioqKlw3ay42YSEjOyQiMSg9KnpTImYmNCUpISM7NyQkIjFtbW07V1RBZSEjOyQiMSZwM3NJZiw4KSEjOzckJCIxKioqKlxpISozYGkhIzskIjFjW0psS3gueSEjOzckJCIxTUxMTCp6eW0nISM7JCIwSk0mb1haX3UhIzo3JCQiMUxMTDNOMSM0KCEjOyQiMSUpUT8pZTQrMCghIzs3JCQiMW1tO0hZdDd2ISM7JCIxX1RoJFs1KipmJyEjOzckJCIpeEcqKnkhIikkIjAoeWlDaCk+OCchIzo3JCQiMW1tbVQ2S1UkKSEjOyQiMUAseSFRTVReJiEjOzckJCIxTExMTGJkUSgpISM7JCIyYykqb1pTPz0nWyEjPDckJCIxbm0ielc/KVwqKSEjOyQiMWUvRkU7LWhXISM7NyQkIixET2w1OyohIzYkIjBQTz5EXCQ0UyEjOjckJCIpUERqJCohIikkIjEiKVJRXGZMNk4hIzs3JCQiLHYuVWFjKiEjNiQiMSJHKWZoTihlIkghIzs3JCQiLkQiRzozdScqISM4JCIyJ0c7QnE7QUtEISM8NyQkIi12PTVzI3kqISM3JCIxdk8+VTREdD8hIzs3JCQiL0QxazIvUCkqISM5JCIyUFZ1ZUxeenoiISM8NyQkIi52JDQwTyIqKSohIzgkIjFILmYlb0grWiIhIzs3JCQiMV43LiNRPyY9KiohIzskIjJCPnpeKj0mUkYiISM8NyQkIi92b2Etb1gqKiEjOSQiMVAlXDhIJykzLyIhIzs3JCQiMHZWdDdTRygqKiEjOiQiMSY9aEoqcD1sdCEjPDckJCIjNSEiIiQiIiEhIiItJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKlRISUNLTkVTU0c2IyIiJi0lJ0NVUlZFU0c2JTdlbjckJCEjNSEiIiQiK1lweFM9ISM1NyQkISpZRz95KiEiKiQiKzJFUyhRIyEjNTckJCErPHAwayYqISM1JCIrOk9nL0ghIzU3JCQhK1g1U3UkKiEjNSQiKi4kZUpMISIqNyQkIStyXnUlPSohIzUkIisuXiJ6dCQhIzU3JCQhKzB0WHIqKSEjNSQiK1BUN3JUISM1NyQkIStVJXAiZSgpISM1JCIrJEdwLGUlISM1NyQkIStseFlWJikhIzUkIisqekkmb1whIzU3JCQhKyM0bShHJCkhIzUkIipsNVdMJiEiKjckJCErQE9TLHohIzUkIis8KSplKipmISM1NyQkISsvUj0wdiEjNSQiK2ltYFlsISM1NyQkIStQOCNcNCghIzUkIitwIT0jW3EhIzU3JCQhKy9zaXFtISM1JCIrbD4sL3YhIzU3JCQhKyh5JHBaaSEjNSQiK3l5YCt6ISM1NyQkISskeWFFImUhIzUkIis5NzxhIykhIzU3JCQhKyI+cyVIYSEjNSQiKydcSllfKSEjNTckJCEqTio0KSpcISIqJCIrI3ovenkpISM1NyQkISpEYlxjJSEiKiQiKzgmW0ksKiEjNTckJCEqbFN2OSUhIiokIitIKltxPiohIzU3JCQhKy8jKVtvUCEjNSQiKzMyQ1IkKiEjNTckJCErJD1leEokISM1JCIrY20uIlsqISM1NyQkIStMMiRmJEghIzUkIilMZyFlKiEiKTckJCErUFl4IlwjISM1JCIrKnpOYm4qISM1NyQkIStMN2kpNCMhIzUkIitoeSNIdSohIzU3JCQhK1AncHNtIiEjNSQiKypHJiozISkqISM1NyQkISs3NF9jNyEjNSQiKzI4NlUpKiEjNTckJCEqM3gleiMpISM1JCIrJm9tPSgpKiEjNTckJCEpcyRRTSUhIiokIitAMDMpKSkqISM1NyQkISgienIpKiEjNSQiK1dIPCUqKSohIzU3JCQiKG8ySiUhIikkIitNSzwpKSkqISM1NyQkIiklUSNcIikhIiokIispKilwRCgpKiEjNTckJCIqOypbSDchIiokIitga1BXKSohIzU3JCQiKWR4ZDshIikkIitBbCo+ISkqISM1NyQkIipgcW4yIyEiKiQiK3c2RFkoKiEjNTckJCIqY3BAWyMhIiokIitzLk94JyohIzU3JCQiKjMnSEtIISIqJCIrT3lZImUqISM1NyQkIip4YW5MJCEiKiQiK2w+aHYlKiEjNTckJCIqdisnb1AhIiokIip1LCNSJCohIio3JCQiKXUiKmZUISIpJCIrW0ItIz4qISM1NyQkIiomKUh4ZSUhIiokIitHWjYtISohIzU3JCQiKi5vLSpcISIqJCIrditKI3opISM1NyQkIipUTzVUJiEiKiQiKyl5Vm5gKSEjNTckJCIqVTlDI2UhIiokIitNIyp6WSMpISM1NyQkIioxKjNgaSEiKiQiK00pPWUqeSEjNTckJCIqJCp6eW0nISIqJCIrd3Z3MXYhIzU3JCQiKl5qPzQoISIqJCIrIm8mXF5xISM1NyQkIipqTUZeKCEiKiQiK2VacU9sISM1NyQkIil4RyoqeSEiKSQiK2BNby1nISM1NyQkIio5QEJNKSEiKiQiK0t0Jj5KJiEjNTckJCIrTiRbL2EpISM1JCIrbylIUShcISM1NyQkIipgdiZRKCkhIiokIitMKXBsaCUhIzU3JCQiK1gvIylcKikhIzUkIisvUnE4VSEjNTckJCIqT2w1OyohIiokIitfXkIoeSQhIzU3JCQiKVBEaiQqISIpJCIrdChIZ04kISM1NyQkIiovVWFjKiEiKiQiK2N1UyxIISM1NyQkIiotQEZ5KiEiKiQiK09JciZRIyEjNTckJCIjNSEiIiQiK1lweFM9ISM1LSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJSpUSElDS05FU1NHNiMiIiMtJSVWSUVXRzYkOyQhIzUhIiIkIiM1ISIiJShERUZBVUxURy0lKkFYRVNTVFlMRUc2IyUnTk9STUFMRy0lKFNDQUxJTkdHNiMlLENPTlNUUkFJTkVERy0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJEkiISIiLSUpQk9VTkRTX1lHNiMkIiVdNSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJXFQISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJSs+ISIiLSUpQ0hJTERSRU5HNiI=

Figura 4 Gr\303\241ficos de 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 (em preto) e uma soma parcial de suas s\303\251ries de Fourier-Legendre (em vermelho) Uma fun\303\247\303\243o integr\303\241vel 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 ser representada pela s\303\251rie de Fourier-Legendre 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onde 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 A fun\303\247\303\243o 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 possui para seus coeficientes de Fourier-Legendre os n\303\272meros 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LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIiIiIhNyNGMQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIjLCQqJiMiIiYiI0siIiJJI1BpR0YmRjYhIiI3I0Yx

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIkIiIhNyNGMQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIlLCQqJiMiIioiJGMjIiIiSSNQaUdGJkY2ISIiNyNGMQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiImIiIhNyNGMQ==

e para uma soma parcial de sua s\303\251rie de Fourier-Legendre, o polin\303\264mio 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRGTGdHRigsJCooIyIjOiIlWz8iIiJJI1BpR0YmRjMsKCIjViEiIiomIiM5RjMpLUkkY29zR0YlNiNJKSZ2YXJwaGk7R0YoIiIjRjNGMyomIiNARjMpRjsiIiVGM0YzRjNGNzcjRi4=

A Figura 5 compara gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== e a soma parcial de sua s\303\251rie de Fourier-Legendre. 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

Figura 5 Gr\303\241ficos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTgxO0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj8tSSNtb0dGJDYtUSI9RidGPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtRiw2JVEkc2luRidGPUY/RjVGPw== (em preto) e uma soma parcial de suas s\303\251ries de Fourier-Legendre (em vermelho)

Sem simetria, 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ent\303\243o a forma separada da solu\303\247\303\243o da equa\303\247\303\243o de Laplace poderia ser 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJVR0YoKigtSSRSaG9HRig2I0kkcmhvR0YoIiIiLUkkUGhpR0YoNiNJKSZ2YXJwaGk7R0YoRjMtSSZUaGV0YUdGKDYjSSZ0aGV0YUdGKEYzNyNGLg==

O Maple providencia as seguintes EDOs governando essas tr\303\252s fun\303\247\303\265es. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEocGRzb2x2ZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRI0xFRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI7RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnRj1GQA==

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

Procedemos para obter esses resultados a partir dos primeiros princ\303\255pios. Em consequ\303\252ncia da divis\303\243o por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e da multiplica\303\247\303\243o por 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a equa\303\247\303\243o de Laplace se torna 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

Se os termos contendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy s\303\243o movidos para a direita, temos 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM5LywqKiwiIiMiIiJJJHJob0dGKEY1KS1JJHNpbkdGJTYjSSkmdmFycGhpO0dGKEY0RjUtSSRSaG9HRig2I0Y2ISIiLUklZGlmZkdGJjYkRjxGNkY1RjUqKilGNkY0RjVGN0Y1RjxGPy1GQTYkRjwtSSIkR0YmNiRGNkY0RjVGNSoqRjhGNS1JJFBoaUdGKEY6Rj8tSSRjb3NHRiVGOkY1LUZBNiRGS0Y7RjVGNSooRjdGNUZLRj8tRkE2JEZLLUZINiRGO0Y0RjVGNSwkKiYtSSZUaGV0YUdGKDYjSSZ0aGV0YUdGKEY/LUZBNiRGWC1GSDYkRmVuRjRGNUY/NyMvLCpGM0Y1KipGREY1RjdGNUY8Rj8tRkE2JEZARjZGNUY1RkpGNSooRjdGNUZLRj8tRkE2JEZPRjtGNUY1LCQqJkZYRj8tRkE2JC1GQTYkRlhGZW5GZW5GNUY/

Introduzindo a constante de separa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy leva \303\240s duas equa\303\247\303\265es 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM6LywqKiwiIiMiIiJJJHJob0dGKEY1KS1JJHNpbkdGJTYjSSkmdmFycGhpO0dGKEY0RjUtSSRSaG9HRig2I0Y2ISIiLUklZGlmZkdGJjYkRjxGNkY1RjUqKilGNkY0RjVGN0Y1RjxGPy1GQTYkRjwtSSIkR0YmNiRGNkY0RjVGNSoqRjhGNS1JJFBoaUdGKEY6Rj8tSSRjb3NHRiVGOkY1LUZBNiRGS0Y7RjVGNSooRjdGNUZLRj8tRkE2JEZLLUZINiRGO0Y0RjVGNUkjbXVHRig3Iy8sKkYzRjUqKkZERjVGN0Y1RjxGPy1GQTYkRkBGNkY1RjVGSkY1KihGN0Y1RktGPy1GQTYkRk9GO0Y1RjVGVg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM7LywkKiYtSSZUaGV0YUdGKDYjSSZ0aGV0YUdGKCEiIi1JJWRpZmZHRiY2JEY0LUkiJEdGJjYkRjciIiMiIiJGOEkjbXVHRig3Iy8sJComRjRGOC1GOjYkLUY6NiRGNEY3RjdGQEY4RkE=

A equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy resultante pode ser colocada na forma 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM8LywmLUklZGlmZkdGJjYkLUkmVGhldGFHRig2I0kmdGhldGFHRigtSSIkR0YmNiRGOSIiIyIiIiomRjZGPkkjbXVHRihGPkY+IiIhNyMvLCYtRjQ2JC1GNDYkRjZGOUY5Rj5GP0Y+RkE=

A continuidade requer a imposi\303\247\303\243o das condi\303\247\303\265es limite peri\303\263dicas 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 dessa forma formando um problema de autovalor de Sturm-Liouville para o qual a solu\303\247\303\243o \303\251 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 Assim, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJW1zdXBHRiQ2JS1GLDYlUSJuRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjJGJ0YyRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjI=. Fazendo essa mudan\303\247a na equa\303\247\303\243o companheira, e dividindo por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnRjVGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRi82JVEnJiM5NjY7RidGMkY1LUkjbW9HRiQ2LVEiLEYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0Y1temos 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM9LywqKioiIiMiIiJJJHJob0dGKEY1LUkkUmhvR0YoNiNGNiEiIi1JJWRpZmZHRiY2JEY3RjZGNUY1KigpRjZGNEY1RjdGOi1GPDYkRjctSSIkR0YmNiRGNkY0RjVGNSoqLUkkUGhpR0YoNiNJKSZ2YXJwaGk7R0YoRjotSSRzaW5HRiVGSEY6LUkkY29zR0YlRkhGNS1GPDYkRkZGSUY1RjUqJkZGRjotRjw2JEZGLUZDNiRGSUY0RjVGNSomKUZKRjRGOilJIm5HRihGNEY1NyMvLCpGM0Y1KihGP0Y1RjdGOi1GPDYkRjtGNkY1RjVGRUY1KiZGRkY6LUY8NiRGTkZJRjVGNUZV

Isolando os termos em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy produz a equa\303\247\303\243o separada 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEjMTlGJy9GNlEnbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSomY29sb25lcTtGJ0Y+LyUmZmVuY2VHRkIvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWi1GLDYlRi4tRiM2JS1GOzYkUSMxOEYnRj5GQEY+RkMtRkc2LVEoJm1pbnVzO0YnRj5GSkZMRk5GUEZSRlRGVi9GWVEsMC4yMjIyMjIyZW1GJy9GZm5GYm8tRi82JVEldGVtcEYnRjJGNUZARj4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM+LywmKioiIiMiIiJJJHJob0dGKEY1LUkkUmhvR0YoNiNGNiEiIi1JJWRpZmZHRiY2JEY3RjZGNUY1KigpRjZGNEY1RjdGOi1GPDYkRjctSSIkR0YmNiRGNkY0RjVGNSwoKiYpLUkkc2luR0YlNiNJKSZ2YXJwaGk7R0YoRjRGOilJIm5HRihGNEY1RjUqKi1JJFBoaUdGKEZKRjpGSEY6LUkkY29zR0YlRkpGNS1GPDYkRk9GS0Y1RjoqJkZPRjotRjw2JEZPLUZDNiRGS0Y0RjVGOjcjLywmRjNGNSooRj9GNUY3RjotRjw2JEY7RjZGNUY1LChGRkY1Rk5GOiomRk9GOi1GPDYkRlNGS0Y1Rjo=

e introduz a constante de separa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy levando \303\240s duas EDOs 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiM/LywmKioiIiMiIiJJJHJob0dGKEY1LUkkUmhvR0YoNiNGNiEiIi1JJWRpZmZHRiY2JEY3RjZGNUY1KigpRjZGNEY1RjdGOi1GPDYkRjctSSIkR0YmNiRGNkY0RjVGNUknbGFtYmRhR0YoNyMvLCZGM0Y1KihGP0Y1RjdGOi1GPDYkRjtGNkY1RjVGRQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiNALywoKiYpLUkkc2luR0YlNiNJKSZ2YXJwaGk7R0YoIiIjISIiKUkibkdGKEY5IiIiRj0qKi1JJFBoaUdGKEY3RjpGNUY6LUkkY29zR0YlRjdGPS1JJWRpZmZHRiY2JEY/RjhGPUY6KiZGP0Y6LUZENiRGPy1JIiRHRiY2JEY4RjlGPUY6SSdsYW1iZGFHRig3Iy8sKEYzRj1GPkY6KiZGP0Y6LUZENiRGQ0Y4Rj1GOkZM

A equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy pode ser manipulada da forma 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiNBLywoKigiIiMiIiJJJHJob0dGKEY1LUklZGlmZkdGJjYkLUkkUmhvR0YoNiNGNkY2RjVGNSomKUY2RjRGNS1GODYkRjotSSIkR0YmNiRGNkY0RjVGNSomRjpGNUknbGFtYmRhR0YoRjUhIiIiIiE3Iy8sKEYzRjUqJkY+RjUtRjg2JEY3RjZGNUY1RkRGRkZH

do qual vemos que \303\251 uma equa\303\247\303\243o de Euler sol\303\272vel em pot\303\252ncias de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy. A EDO remanescente \303\251 associada \303\240 equa\303\247\303\243 de Legendre, que moldamos na forma 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiNCLywqKigtSSRzaW5HRiU2I0kpJnZhcnBoaTtHRighIiItSSRQaGlHRihGNiIiIilJIm5HRigiIiNGO0Y7KiYtSSRjb3NHRiVGNkY7LUklZGlmZkdGJjYkRjlGN0Y7RjgqJkY0RjstRkM2JEY5LUkiJEdGJjYkRjdGPkY7RjgqKEY5RjtGNEY7SSdsYW1iZGFHRihGO0Y4IiIhNyMvLCpGM0Y7Rj9GOComRjRGOy1GQzYkRkJGN0Y7RjhGS0Y4Rk0=

trazendo todos ops termos para a esquerda e multiplicando por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY2O0YnRi9GMkYyRjItRiw2JVEkY29zRidGL0YyRjUtSSNtb0dGJDYtUSIuRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlRGMg== A mesma mudan\303\247a de vari\303\241veis que foi usada para a equa\303\247\303\243o de Legendre \303\251 aplicada, levando a 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiNDLywkKiYsMiomLUkieUdGKDYjSSJ4R0YoIiIiKUkibkdGKCIiI0Y6RjoqKEY9RjotSSVkaWZmR0YmNiRGNkY5RjpGOUY6RjoqKEY9RjopRjkiIiRGOkY/RjohIiItRkA2JEY2LUkiJEdGJjYkRjlGPUZFKihGPUY6RkZGOilGOUY9RjpGOiomRkZGOilGOSIiJUY6RkUqJkY2RjpJJ2xhbWJkYUdGKEY6RkUqKEY2RjpGUUY6RkxGOkY6RjopLCZGOkY6KiRGTEY6RkUjRjpGPUZFRkUiIiE3Iy8sJComLDJGNUY6Rj5GOkZCRkUtRkA2JEY/RjlGRSooRj1GOkZnbkY6RkxGOkY6KiZGZ25GOkZORjpGRUZQRkVGUkY6RjpGU0ZFRkVGVw==

e ent\303\243o 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCgqJiwmIiIiRjAqJClJInhHRigiIiNGMCEiIkYwLUklZGlmZkdGJjYkLUkieUdGKDYjRjMtSSIkR0YmNiRGM0Y0RjBGMCooRjRGMC1GNzYkRjlGM0YwRjNGMEY1KigsKCokKUkibkdGKEY0RjBGMComSSdsYW1iZGFHRihGMEYyRjBGMEZIRjVGMCwmRjBGNUYxRjBGNUY5RjBGMCIiITcjLywoKiZGL0YwLUY3NiRGQEYzRjBGMEY/RjVGQkYwRko=

ap\303\263s o rearranjo apropriado. Uma forma ligeiramente melhor para essa equa\303\247\303\243o pode ser obtida com o comando 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkicUdGKDYjIiNELywoKiYsJiIiIkY1KiQpSSJ4R0YoIiIjRjUhIiJGNS1JJWRpZmZHRiY2JC1JInlHRig2I0Y4LUkiJEdGJjYkRjhGOUY1RjUqKEY5RjUtRjw2JEY+RjhGNUY4RjVGOiomLCZJJ2xhbWJkYUdGKEY1KiYpSSJuR0YoRjlGNSwmRjVGOkY2RjVGOkY1RjVGPkY1RjUiIiE3Iy8sKComRjRGNS1GPDYkRkVGOEY1RjVGREY6RkdGNUZO

mas a forma tipicamente vista da equa\303\247\303\243o associada de Legendre \303\251 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

A solu\303\247\303\243o geral da equa\303\247\303\243o associada de Legendre \303\251 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

Ly1JInlHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JKkxlZ2VuZHJlUEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYlLCYqJiNGKyIiI0YrKSwmKiYiIiVGK0knbGFtYmRhR0YlRitGK0YrRitGNEYrRitGNCEiIkkibkdGJUYnRitGKyomSSRfQzJHRiVGKy1JKkxlZ2VuZHJlUUdGLkYxRitGKw==

uma combina\303\247\303\243o linear das duas fun\303\247\303\265es associadas de Legendre, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRj1GP0ZBLUYsNiVRInhGJ0Y9Rj9GMkYyRjI= e 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 (No modo prorrogado de composi\303\247\303\243o, o Maple escreve essas fun\303\247\303\265es como 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e 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respectivamente.) Essas s\303\243o imaginativamente chamadas fun\303\247\303\265es associadas de Legendre de primeiro e segundo tipos, respectivamente. Das equa\303\247\303\265es associadas de Legendre podemos ver que 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e 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 No plano complexo, In the complex plane, um ramo de corte para uma fun\303\247\303\243o \303\251 uma reta ou segmento de reta sobre o qual a fun\303\247\303\243o possui uma descontinuidade de salto. No Maple, existem dois regimes de corte para as fun\303\247\303\265es de Legendre. O regime padr\303\243o imp\303\265e um corte na reta real coincidente com o intervalo 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 Alternativamente, os intervalos reais 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 e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjg2LVEoJmluZmluO0YnRjRGOy9GP0Y9RkFGQ0ZFRkdGSUZLL0ZPRk1GNEY0RjQ= incluem um segundo regime de corte. A vari\303\241vel de ambiente _EnvLegendreCut \303\251 usada para reparar o regime de corte atribuindo-o a cada uma das express\303\265es -1..1 ou 1..infinito. Para resolver a equa\303\247\303\243o de Laplace no interior de uma esfera, as fun\303\247\303\265es associadas de Legendre que surgem devem possuir seus ramos de corte fora do intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRidGS0Y0RjRGT0Y0isto \303\251, opostos ao regime padr\303\243o. Portanto, quando trabalhando no Maple, o ramo de corte deve ser mudado por meio de uma atribui\303\247\303\243o para as vari\303\241veis de ambiente. Entretanto, comandos como evalf ou simplify, comandos que ir\303\243o provavelmente ser convocados no contexto do processo de solu\303\247\303\243o, possuem uma tabela de lembran\303\247a, que armazena o valor atribu\303\255do \303\240 vari\303\241vel de ambiente. Reatribuindo um novo valor \303\240 vari\303\241vel de ambiente n\303\243o ir\303\241 mudar o regime de corte a menos que algo seja feito para modificar a tabela de lembran\303\247a em comandos como evalf e simplify. Isso \303\251 feito aplicando o comando forget a esses operadores antes de mudar a atribui\303\247\303\243o para as vari\303\241veis de ambiente. Por uma quest\303\243o de integridade, ilustramos essas quest\303\265es abaixo. Com o corte padr\303\243o no lugar, a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUkjbW5HRiQ2JFEiNUYnRjItSSNtb0dGJDYtUSIsRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjNGJ0YyRj4tRiw2JVEieEYnL0YwRkYvRjNRJ2l0YWxpY0YnRjJGMkYy \303\251 descont\303\255nua atrav\303\251s do segmento de reta coincidente com o intervalo real LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRidGS0Y0RjRGT0Y0uma descontinuidade que exemplificamos em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJDAuNkYnRjlGOQ== com as avalia\303\247\303\265es 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

LCYkIisrK2c0NyEjOyIiIiomJCIrKys3QGchIilGJl4jRiZGJiEiIg==

LCYkIisrK2c0NyEjOyIiIiomJCIrKys3QGchIilGJl4jRiZGJkYm

Outro modo de ver a descontinuidade atrav\303\251s desse corte \303\251 simbolicamente, com 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

LCQqKiMiJDAiIiIjIiIiKSwmRichIiJJInhHNiJGJyMiIiRGJkYnKSwmRitGJ0YnRidGLUYnLCZGJ0YqKiYiIipGJylGK0YmRidGJ0YnRic=

Uma inspe\303\247\303\243o cuidadosa mostra que para 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, o termo 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 ser\303\241 a raiz quadrada de um n\303\272mero negativo, de onde a descontinuidade 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

LCQqJiwkXiMiIiJGJkYmKSwmRiZGJkkieEc2IiEiIiMiIiQiIiNGJkYr

KiZeIyIiIkYkKSwmRiRGJEkieEc2IiEiIiMiIiQiIiNGJA==

surge. Agora, se tentarmos mudar o ramo de corte com 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 pode parecer que o comportamento de simplify \303\251 err\303\241dico; simplify pode ou n\303\243o refletir a mudan\303\247a no ramo de corte, dependendo do estado interno do Maple, Aqui, vemos 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

LCQqKiMiJDAiIiIjIiIiKSwmRichIiJJInhHNiJGJyMiIiRGJkYnKSwmRitGJ0YnRidGLUYnLCZGJ0YqKiYiIipGJylGK0YmRidGJ0YnRic=

Portanto, \303\251 poss\303\255vel que poder\303\255amos obter exatamente o mesmo resultado que quando o ramo de corte \303\251 ao longo de 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 A raz\303\243o para a incerteza repousa na tabela de lembran\303\247a anexada ao comando simplify. Embora a reatribui\303\247\303\243o para a vari\303\241vel de ambiente \303\251 imediata, por causa da tabela de lembran\303\247a simplify n\303\243o ir\303\241 imediatamente acessar o novo valor a menos que um evento interno fa\303\247a com que a tabela seja limpa. Para for\303\247ar a tabela de lembran\303\247a a acessar uma nova atribui\303\247\303\243o, use 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 o efeito do qual testamos via 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

LCQqKiMiJDAiIiIjIiIiKSwmRidGJ0kieEc2IiEiIiMiIiRGJkYnKSwmRipGJ0YnRidGLUYnLCZGJ0YsKiYiIipGJylGKkYmRidGJ0YnRiw=

Em ambos os eventos note que o termo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUYjNiQtSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiQtRiM2Ji1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSgmbWludXM7RidGPy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GQFEnaXRhbGljRidGP0Y/LUYjNiYtRjw2JFEiM0YnRj8tRkM2LVEiL0YnRj9GRkZJL0ZMRmluRk1GT0ZRRlMvRlZRLDAuMTY2NjY2N2VtRicvRllGZm8tRjw2JFEiMkYnRj9GPy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGP0YrRj9GK0Y/ \303\251 real para 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e n\303\243o haver\303\241 um salto atrav\303\251s de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JI21uR0YkNiRRIjFGJ0Y0LUYxNi1RIixGJ0Y0RjcvRjtRJXRydWVGJ0Y8Rj5GQEZCRkQvRkdRJjAuMGVtRicvRkpRLDAuMzMzMzMzM2VtRidGS0Y0RjRGT0Y0como vemos por 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

KiQpLCYiIiJGJUkieEc2IiEiIiMiIiQiIiNGJQ==

KiQpLCYiIiJGJUkieEc2IiEiIiMiIiQiIiNGJQ==

A fun\303\247\303\243o associada de Legendre de primeiro tipo aparece nos livros-texto com dois s\303\255mbolos diferentes. Por exemplo, no Handbook of Mathematical Functions de Abramowitz e Stegun (Dover Publications), encontramos as seguintes duas f\303\263rmulas relacionando essas fun\303\247\303\265es aos polin\303\264mios de Legendre. 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 Por experimentos \303\263bvios, podemos concluir que no Maple 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 De fato, constru\303\255mos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobXN1YnN1cEdGJDYoLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiNUYnL0Y2USdub3JtYWxGJ0Y+LUYjNiQtRjs2JFEiM0YnRj5GPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGRy9JK21zZW1hbnRpY3NHRiRRLFtub25lLG5vbmVdRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGMkY1Rj5GPkY+ como 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

LCQqJiksJiIiIkYmKiQpSSJ4RzYiIiIjRiYhIiIjIiIkRitGJiwmKiYjIiRYKkYrRiZGKEYmRiYjIiQwIkYrRixGJkYs

e o comparamos \303\240 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqTGVnZW5kcmVQRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUkjbW5HRiQ2JFEiNUYnRjItSSNtb0dGJDYtUSIsRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjNGJ0YyRj4tRiw2JVEieEYnL0YwRkYvRjNRJ2l0YWxpY0YnRjJGMkYy na forma 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

LCQqKiMiJDAiIiIjIiIiKSwmRidGJ0kieEc2IiEiIiMiIiRGJkYnKSwmRipGJ0YnRidGLUYnLCZGJ0YsKiYiIipGJylGKkYmRidGJ0YnRiw=

Em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy1GLDYtUSYmbGVxO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZOLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZKRkZGLw==, os radicais que aparecem em ambas express\303\265es s\303\243o equivalentes, como demonstrado pelos gr\303\241ficos na Figura 6. 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

Figura 6 Gr\303\241ficos de 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 (vermelho) e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobXN1YnN1cEdGJDYoLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiNUYnL0Y2USdub3JtYWxGJ0Y+LUYjNiQtRjs2JFEiM0YnRj5GPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGRy9JK21zZW1hbnRpY3NHRiRRLFtub25lLG5vbmVdRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGMkY1Rj5GPkY+ (preto)

A rela\303\247\303\243o de ortogonalidade para as fun\303\247\303\265es associadas de Legendre de primeiro tipo \303\251 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 uma rela\303\247\303\243o que o Maple pode fundamentar, mas n\303\243o facilmente estabelecer a partir de princ\303\255pios iniciais. Por exemplo, a Tabela 2 lista algumas integrais para as quais LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJuRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRidGOQ==enquanto a Tabela 3 lista algumas para as quais LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJuRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRidGOQ==comparando os valores computados e formulados da integral. 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Ly1JJEludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkiLkdGJTYkLUkqTGVnZW5kcmVQR0YlNiUiIiQiIiJJInhHRigtRi42JSIiI0YxRjIvRjI7ISIiRjEiIiE=

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Tabela 2 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 for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKyZOb3RFcXVhbDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJuRidGL0YyRjk= Tabela 3 Para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJuRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRidGOQ==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 a 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

As fun\303\247\303\265es 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com as fun\303\247\303\265es 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formam um conjunto completo no ret\303\242ngulo 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 Consequentemente, uma fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRJyYjOTY2O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y/LyUmZmVuY2VHRj4vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NTI7RidGPUY/Rj9GP0Y/ pode ser exoandida em uma s\303\251rie de Fourier-Legendre da forma 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 Por exemplo, pegue LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRJyYjOTY2O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y/LyUmZmVuY2VHRj4vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NTI7RidGPUY/Rj9GP0Y/ como 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJnR0YoLCQqLCMiIiIiIidGMUkpJnZhcnBoaTtHRihGMSwmSSNQaUdGJkYxRjMhIiJGMUkmdGhldGFHRihGMSwmKiYiIiNGMUY1RjFGMUY3RjZGMUYxNyNGLg==

uma fun\303\247\303\243o cujo gr\303\241fico \303\251 visto na Figura 7. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEncGxvdDNkRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2MVEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUSZzZXJpZkYnLyUlYm9sZEdGOC8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y6USVib2xkRicvJStmb250d2VpZ2h0R0ZJLyUmZmVuY2VHRkcvJSpzZXBhcmF0b3JHRkcvJSlzdHJldGNoeUdGRy8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGZm4tSShtZmVuY2VkR0YkNiQtRiM2RS1GLDYlUSJnRidGNkY5LUY9Ni1RIixGJy9GOlEnbm9ybWFsRidGTC9GT0Y4RlBGUkZURlZGWEZaL0ZoblEsMC4zMzMzMzMzZW1GJy1GLDYlUScmIzk2NjtGJy9GN0ZHRmRvLUY9Ni1RIj1GJ0Zkb0ZMRk5GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GYXAtSSNtbkdGJDYkUSIwRidGZG8tRj02LVEjLi5GJ0Zkb0ZMRk5GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJ0Znbi1GLDYlUScmIzk2MDtGJ0ZccEZkb0Zhby1GLDYlUScmIzk1MjtGJ0ZccEZkb0ZdcEZjcEZncC1GZHA2JFEiMkYnRmRvLUY9NjBRMSZJbnZpc2libGVUaW1lcztGJ0ZALyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0ZHRmRvRkxGTkZQRlJGVEZWRlhGWkZnbkZccUZhby1GLDYlUSVheGVzRidGNkY5Rl1wLUYsNiVRJGJveEYnRjZGOUZhby1GLDYlUShzY2FsaW5nRidGNkY5Rl1wLUYsNiVRLGNvbnN0cmFpbmVkRidGNkY5RmFvLUY9Ni1RIn5GJ0Zkb0ZMRk5GUEZSRlRGVkZYRlpGZ24tRiw2JVEnbGFiZWxzRidGNkY5Rl1wLUZqbjYmLUYjNiwtRj02LVEiJ0YnRmRvRkxGTkZQRlJGVEZWRlgvRmVuUSwwLjExMTExMTFlbUYnRmduLUYsNiVRImZGJ0Y2RjlGY3NGYW8tRiw2JVEicUYnRjZGOUZhby1JI21zR0YkNiNGW3NGK0ZFRmRvRmRvLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmFvRmlyLUYsNiVRKmxhYmVsZm9udEYnRjZGOUZdcC1Gam42Ji1GIzYnLUYsNiVRJ1NZTUJPTEYnRjZGOUZhby1GZHA2JFEjMTJGJ0Zkb0ZFRmRvRmRvRmF0RmR0RkVGZG9GZG9GRUZkb0YrRkVGZG9GK0ZFRmRv

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Figura 7 Gr\303\241fico de 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 Tamb\303\251m \303\251 \303\272til para definir a fun\303\247\303\243o 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

Ly1JImRHNiI2JEkia0dGJUkibUdGJSwkKioiIiMiIiItSSpmYWN0b3JpYWxHJSpwcm90ZWN0ZWRHNiMsJkYnRixGKEYsRiwtRi42IywmRidGLEYoISIiRjUsJiomRitGLEYnRixGLEYsRixGNUYs

cujos valores aparecem nos denominadores das express\303\265es para os coeficientes das s\303\251ries. A computa\303\247\303\243o desses coeficientes \303\251 ligeiramente simplificada pelo reconhecimento de que todos os LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRI2ttRidGMkY1L0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRj0= s\303\243o zero por simetria. Ent\303\243o, os primeiros LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRI2swRidGMkY1L0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRj0= s\303\243o dados por 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 e os primeiros 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\303\243o dados por 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 Uma soma parcial da s\303\251rie de Fourier-Legendre para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 ent\303\243o 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 o gr\303\241fico do qual pode ser visto na Figura 8. 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Figura 8 Gr\303\241fico da soma parcial da s\303\251rie de Fourier-Legendre para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRJyYjOTgxO0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y/LyUmZmVuY2VHRj4vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NTI7RidGPUY/Rj9GP0Y/ Para estimar a exatid\303\243o dessa aproxima\303\247\303\243o, a diferen\303\247a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJnRidGL0YyRjk= \303\251 constru\303\255da na Figura 9. 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Figura 9 Gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJnRidGL0YyRjk= como uma estimativa da exatid\303\243o da soma parcial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=

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