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

GUO Dong-wei, CHEN Yu-lei

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

Chinese Quarterly Journal of Mathematics >

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

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

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,

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.

Received date: 2021-08-10

Online published: 2022-03-30

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Abstract

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).

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

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GUO Dong-wei, CHEN Yu-lei . Expressions of Two Classes of Infinite Series in Terms of Bernoulli Numbers[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(1) : 79 -87 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.01.008

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