Chunli Li, Wenchang Chu, “Integral Representations of <nobr>$\mathrm{\zeta}(m)$</nobr>”, Mat. Zametki, 2024, Volume 115, Issue 4,Pages <nobr>569

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Papers published in the English version of the journal

Integral Representations of $\mathrm{\zeta}(m)$

Chunli Li^a, Wenchang Chu^b

^a School of Mathematics and Statistics, Zhoukou Normal University, P. R. China
^b Lecce University, Italy

Abstract: An open problem about integral representation of $\zeta(2n)$, proposed recently by Pain (2023), is resolved by integration by parts. More general integrals are examined by manipulating the beta integral and digamma function.

Keywords: Riemann zeta function, generating function, beta integral, digamma function.

Received: 28.11.2023
Revised: 13.01.2024

Language: English