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Números e Polinômios de Bernoulli

Números e Polinômios de Bernoulli

Maikon Luiz Mirkoski

54,25 €
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Editorial:
KS OmniScriptum Publishing
Año de edición:
2024
Materia
Matemáticas
ISBN:
9786206760597
54,25 €
IVA incluido
Disponible

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Sobre IBD

Nesta dissertação tivemos como objetivo explorar algumas das conexões mais importantes entre os números e os polinómios de Bernoulli e as funções zeta, gama e teta. De forma mais detalhada, no capítulo 2 introduzimos os polinómios de Bernoulli mostrando que são os únicos polinómios que satisfazem três condições simples. Já os números de Bernoulli foram definidos como sendo os valores em x = 0 dos correspondentes polinomios de Bernoulli. A seguir mostramos como a sequência dos números de Bernoulli pode ser obtida de maneira recursiva. Por fim ilustramos esse resultado calculando os primeiros números de Bernoulli. No capítulo 3 calculamos as séries de Fourier para os polinómios de Bernoulli no intervalo [0,1]. A seguir definimos a funcão zeta de Riemann e provamos a equação de Euler que relaciona esta funcão com os números primos. Por fim, utilizamos as séries de Fourier obtidas anteriormente para expressar o valor da funcão zeta nos pares positivos em termos de numeros de Bernoulli. No capítulo 4 estudamos série de potência que geram os números e os polinómios de Bernoulli.

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