两类无穷级数的Bernoulli数表示

郭东威, 陈玉磊

doi:10.13371/j.cnki.chin.q.j.m.2022.01.008

数学季刊 >

2022 , Vol. 37 >Issue 1: 79 - 87

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.01.008

两类无穷级数的Bernoulli数表示

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1. School of Mathematics and Statistics, Zhoukou Normal University,
2. School of Mathematics and Statistics, Wuhan University,

GUO Dong-wei (1987-), male, native of Kaifeng, Henan, lecturer of Zhoukou Normal University, engages in combinatorial mathematics; CHEN Yu-lei (1989-), female, native of Zhoukou, Henan, Ph.D. student of Wuhan University, engages in number theory and cryptography.

收稿日期: 2021-08-10

网络出版日期: 2022-03-30

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Expressions of Two Classes of Infinite Series in Terms of Bernoulli Numbers

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1. School of Mathematics and Statistics, Zhoukou Normal University,
2. School of Mathematics and Statistics, Wuhan University,

Received date: 2021-08-10

Online published: 2022-03-30

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摘要

In this paper, the expressions of two classes of infinite series in terms of finite series involving Bernoulli numbers are obtained. As applications, we derive some special series including Dirichlet beta function β ( s ) with argument 2 n +1 and Dirichlet lambda function λ ( s ) with argument 2 n . In addition, we solve the problem proposed recently by Zhou (2021).

关键词： Bernoulli numbers; Bernoulli polynomials; Polygamma function; Generalized Zeta function

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郭东威, 陈玉磊 . 两类无穷级数的Bernoulli数表示[J]. 数学季刊, 2022 , 37(1) : 79 -87 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.008

Abstract

Key words： Bernoulli numbers; Bernoulli polynomials; Polygamma function; Generalized Zeta function

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