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

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030283

Chunli Li, Wenchang Chu

引用次数: 0

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.

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$$\mathrm{\zeta}(m)$$ 的积分表示法

摘要 Pain (2023)最近提出的一个关于 $\zeta(2n)$ 的积分表示的未决问题，通过分部积分得到了解决。通过操作β积分和digamma函数，研究了更一般的积分。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.