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

  • Received : 2013.04.01
  • Published : 2014.09.30

Abstract

The Euler zeta function is defined by ${\zeta}_E(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^8}$. The purpose of this paper is to find formulas of the Euler zeta function's values. In this paper, for $s{\in}\mathbb{N}$ we find the recurrence formula of ${\zeta}_E(2s)$ using the Fourier series. Also we find the recurrence formula of $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{(2_{n-1})^{2s-1}}$, where $s{\geq}2({\in}\mathbb{N})$.

Keywords

zeta function;Euler zeta function;Fourier series

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Cited by

  1. ON THE RECURRENCE FORMULA OF THE EULER ZETA FUNCTIONS vol.29, pp.2, 2016, https://doi.org/10.14403/jcms.2016.29.2.283

Acknowledgement

Supported by : Hannam University