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<Text-field style="Heading 1" layout="Normal"><Font encoding="UTF-8">expans\303\243o assint\303\263tica,</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">n.</Font><Font encoding="UTF-8"> (de uma fun\303\247\303\243o </Font><Font italic="true">x</Font><Font encoding="UTF-8">) qualquer s\303\251rie divergente na forma </Font></Text-field>
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e tal que para todo <Font italic="true">n</Font> </Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1JJ211bmRlckdGJDYlLUkjbW9HRiQ2LVEkbGltRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dRJXRydWVGJy8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjE2NjY2NjdlbUYnLUYjNiYtRiw2JVEiekYnLyUnaXRhbGljR0ZIL0Y5USdpdGFsaWNGJy1GNTYtUScmcmFycjtGJ0Y4RjtGPkZARkJGRC9GR0Y9RklGSy9GT0ZNLUYsNiVRKCZpbmZpbjtGJ0ZWRlhGOC8lLGFjY2VudHVuZGVyR0Y9RistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuNGVtRicvJSZkZXB0aEdGY28vJSpsaW5lYnJlYWtHUSVhdXRvRictSSVtc3VwR0YkNiVGUy1GLDYlUSJuRidGVkZYLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y4RitGOA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1JJ211bmRlckdGJDYlLUkjbW9HRiQ2LVEkbGltRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dRJXRydWVGJy8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjE2NjY2NjdlbUYnLUYjNiYtRiw2JVEiekYnLyUnaXRhbGljR0ZIL0Y5USdpdGFsaWNGJy1GNTYtUScmcmFycjtGJ0Y4RjtGPkZARkJGRC9GR0Y9RklGSy9GT0ZNLUYsNiVRKCZpbmZpbjtGJ0ZWRlhGOC8lLGFjY2VudHVuZGVyR0Y9RistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuNGVtRicvJSZkZXB0aEdGY28vJSpsaW5lYnJlYWtHUSVhdXRvRictSSVtc3VwR0YkNiVGUy1GLDYlUSJuRidGVkZYLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y4RitGOA==</Equation><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>, 
que podem ser escritos  
<Font italic="true">f</Font>(<Font italic="true">z</Font>) ~ <Font italic="true">a</Font><Font subscript="true">0</Font>  + <Font italic="true">a</Font><Font subscript="true">1</Font>/<Font italic="true">z</Font> + .... 
<Font encoding="UTF-8">Estimativa de graus vari\303\241veis de precis\303\243o por isso produz um papel importante na analize, especialmente com </Font><Font italic="true">n</Font><Font encoding="UTF-8"> = 1.  Duas fun\303\247\303\265es podem ter a mesma expans\303\243o assint\303\263tica; por exemplo, </Font><Font italic="true">e</Font><Font superscript="true">1/<Font italic="true">z</Font></Font> e <Font italic="true">e</Font><Font superscript="true">1/<Font italic="true">z</Font></Font> + <Font italic="true">e<Font superscript="true">-z</Font></Font><Font encoding="UTF-8"> ambas tem a mesma expans\303\243o assint\303\263tica nomeamente  </Font></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>+... 
para |arg <Font italic="true">z</Font>| <Font family="MaplePi">&lt;</Font> <Font family="MaplePi">p</Font>/2.  mais geralmente, se <Font italic="true">f</Font>/<Font italic="true">g</Font><Font encoding="UTF-8"> tem uma expans\303\243o assint\303\263tica, ent\303\243o </Font><Font italic="true">f</Font><Font encoding="UTF-8"> \303\251 assint\303\263tica para seu produto com </Font><Font italic="true">g</Font>. Veja <Hyperlink linktarget="Dictionary:Definition/Stirlingsformula" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">f\303\263rmula de Stirling</Font></Hyperlink>.<Font encoding="UTF-8"> Veja tamb\303\251m </Font><Hyperlink linktarget="Dictionary:Definition,asymptoticexpansiontoNterms" hyperlink="true"><Font style="Dictionary Hyperlink" encoding="UTF-8">expans\303\243o assint\303\263tica para N termos</Font></Hyperlink>.</Text-field>
</Worksheet>