A NOTE ON RECURRENCE FORMULA FOR VALUES OF THE EULER ZETA FUNCTIONS ζE(2n) AT POSITIVE INTEGERS

Title & Authors
A NOTE ON RECURRENCE FORMULA FOR VALUES OF THE EULER ZETA FUNCTIONS ζE(2n) AT POSITIVE INTEGERS
Lee, Hui Young; Ryoo, Cheon Seoung;

Abstract
The Euler zeta function is defined by $\small{{\zeta}_E(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^8}}$. The purpose of this paper is to find formulas of the Euler zeta function's values. In this paper, for $\small{s{\in}\mathbb{N}}$ we find the recurrence formula of $\small{{\zeta}_E(2s)}$ using the Fourier series. Also we find the recurrence formula of $\small{\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{(2_{n-1})^{2s-1}}}$, where $\small{s{\geq}2({\in}\mathbb{N})}$.
Keywords
zeta function;Euler zeta function;Fourier series;
Language
English
Cited by
1.
ON THE RECURRENCE FORMULA OF THE EULER ZETA FUNCTIONS, Journal of the Chungcheong Mathematical Society, 2016, 29, 2, 283
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