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

两类无穷级数的Bernoulli数表示

作　　者：GUO Dong-wei CHEN Yu-lei 郭东威;陈玉磊(School of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466001,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430061,China)

机构地区：[1]School of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466001,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430061,China

出　　处：《Chinese Quarterly Journal of Mathematics》2022年第1期79-87,共9页数学季刊（英文版）

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 functionβ(s)with argument 2n+1 and Dirichlet lambda functionλ(s)with argument 2n.In addition,we solve the problem proposed recently by Zhou(2021).

关 键 词：Bernoulli numbers Bernoulli polynomials Polygamma function Generalized Zeta function 

分 类 号：O157.1[理学—数学]