Computando a constante MRB no Maple JSFH Marvin Ray Burns Investigador original do MRB constnat e outros LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field> A constante MRB est\303\241 relacionada \303\240s seguintes s\303\251ries divergentes: 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Suas somas parciais 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A constante MRB pode ser definida explicitamente pelas seguintes somas infinitas: 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<Text-field style="Heading 2" layout="Heading 2">O objetivo deste documento</Text-field> Mostrar como calcular efetivamente muitos d\303\255gitos da constante MRB no Maple.
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<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Computando a constante atrav\303\251s da for\303\247a bruta</Font></Text-field> Apenas 2 casas decimais corretas da constante MRB podem ser calculadas pelo seguinte comando. ; 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 JCIqeDguKT0hIio= Torna-se \303\263bvio que a for\303\247a bruta n\303\243o \303\251 um m\303\251todo eficaz para calcular a constante MRB em Maple; JSFH
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<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">M\303\251todos de acelera\303\247\303\243o</Font></Text-field>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">Transforma\303\247\303\243o em U de Levin</Font></Text-field> 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 O comando a seguir fornece 500 d\303\255gitos da constante, embora muito lentamente. 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 JCJfamxyTT9LYDAmUk8wUjpfV08rLTN0RjcoRyQpNDAiKj1BQDlyJUgqb1JiYS0hUSllQUFNK1k6Km87a3k7eTpKNU1bKFJqIzRtMTFyQyZ6X1U1V3FPWydlYlU/ayZccF8pbyhcSCJvZTRCVyV5P3I1X1snNE5oYl0kKXpYOVIqKlEqKWZGRCFvKD4mKSo+blROT1svbzclM2FyOzo8aT9Hdz9xQCQqW3JAJ1J3X0RAJEdOTVB6ajdRRmc4OzNFbUxQMzclPScqKVskSCpRL2pFI2ZaNHE4QmghPiFlaSZlTVVRIXBcMkpWYW1ILlBAZ1ljSnNaKjMlby8/PCd5USwhXDQuZjBJS0ZhUyR6XlstN24/WVUnZnk9ISQrJg== JSFH
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251todo de acelera\303\247\303\243o de Cohen / Rodriguez / Zagier, aplicado por Burns</Font></Text-field> O procedimento a seguir calcula 500 d\303\255gitos da constante muito mais r\303\241pido .; 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShBMDM3MDc3RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtSSNtbkdGJDYkUSQ1MDBGJy9GOFEnbm9ybWFsRidGQ0ZDRkNGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRkM= JCJfamwpKVxAS2AwJlJPMFI6X1dPKy0zdEY3KEckKTQwIio9QUA5ciVIKm9SYmEtIVEpZUFBTStZOipvO2t5O3k6SjVNWyhSaiM0bTExckMmel9VNVdxT1snZWJVP2smXHBfKW8oXEgib2U0QlcleT9yNV9bJzROaGJdJCl6WDlSKipRKilmRkQhbyg+JikqPm5UTk9bL283JTNhcjs6PGk/R3c/cUAkKltyQCdSd19EQCRHTk1Qemo3UUZnODszRW1MUDM3JT0nKilbJEgqUS9qRSNmWjRxOEJoIT4hZWkmZU1VUSFwXDJKVmFtSC5QQGdZY0pzWiozJW8vPzwneVEsIVw0LmYwSUtGYVMkel5bLTduP1lVJ2Z5PSEkKyY= JSFH JSFH
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<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">Outros m\303\251todos de acelera\303\247\303\243o</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">M\303\251todo unificado de Crandall</Font></Text-field> http://www.perfscipress.com/papers/UniversalTOC25.pdf JSFH
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