含有高阶广义调和数的无穷级数恒等式  

Infinite Series Identities Containing High-Order Generalized Harmonic Numbers

作　　者：王晓元[1] 孙艾莹 

机构地区：[1]大连交通大学理学院,辽宁 大连

出　　处：《理论数学》2024年第6期178-192,共15页Pure Mathematics

摘　　要：在本文中,定义一类m阶广义调和数利用组合分析中的Abel分部求和法,我们将推导出一些含有2阶广义调和数和3阶广义调和数的无穷级数与交错级数恒等式。进一步对参数a和b取特殊值,获得一些新的关于π,π2,π3,ζ(3),Catalan常数和ln2的无穷级数表达式。In this paper, we define a class of generalized harmonic numbers of order m by  Applying Abel’s method on summation by parts in combination analysis, we shall derive several infinite series and alternating series containing generalized harmonic numbers of order 2 and 3. Furthermore, by selecting special values for parameters a and b, several new infinite series ex-pressions are obtained for π, π2, π3, ζ(3), Catalan constant and ln2 as consequences.

关 键 词：调和数 广义调和数 Abel分部求和法 

分 类 号：O17[理学—数学]