含有调和数平方的无穷级数恒等式  

Infinite Series Identities Involving Quadratic Harmonic Numbers

作　　者：王晓元[1] 刘筱蒙 

机构地区：[1]大连交通大学理学院,辽宁 大连

出　　处：《理论数学》2023年第3期516-525,共10页Pure Mathematics

摘　　要：本文研究两类含有以下广义调和数平方的组合恒等式。首先通过组合分析中的Abel分部求和引理获得含有两个差分对{Ak,Bk}和{Ak′,Bk′}的无穷级数求和公式,即定理2。然后选取恰当的序列{Ak,Ak′}和{Bk,Bk′},利用定理2,证明含有广义调和数hk2(a,b)和hk2(a,b)的无穷级数恒等式。最后对参数a和b取特殊值,进一步获得一些新的π,Catalan常数和ln2的无穷级数求和公式。In this paper, we study two combinatorial identities including the following quadratic generalized harmonic numbers First, the modified Abel lemma on summation by parts in combination analysis is employed to obtain summation formulae of infinite series involving two difference pairs {Ak,Bk} and {Ak′,Bk′}, that is Theorem 2. Then applying Theorem 2 through appropriate sequences {Ak,Ak′} and {Bk,Bk′}, we establish infinite series identities involving generalized harmonic numbers hk2(a,b) and hk2(a,b). Finally, by selecting special values for parameters a and b, several new infinite series are obtained for , Catalan constant and ln2 as consequences.

关 键 词：广义调和数 调和数 调和类数 Abel分部求和引理 

分 类 号：O17[理学—数学]