Integral representations of the Riemann zeta function of odd argument

Jean-Christophe Pain

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arXiv · 2410.23096

Integral representations of the Riemann zeta function of odd argument

Jean-Christophe Pain

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Abstract

In this article we obtain, using an expression of the digamma function $\psi(x)$ due to Mikolas, integral representations of the zeta function of odd arguments $\zeta(2p+1)$ for any positive value of $p$. The integrand consists of the product of a polynomial by one or two elementary trigonometric functions. Examples for the first values of the argument are given. Some of them were already derived by other methods.

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Jean-Christophe Pain. 2024-10-30. Integral representations of the Riemann zeta function of odd argument. https://arxiv.org/abs/2410.23096

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