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
DOI: 10.12677/pm.2024.146239, PDF,    科研立项经费支持
作者: 王晓元, 孙艾莹：大连交通大学理学院，辽宁 大连
关键词: 调和数；广义调和数；Abel分部求和法；Harmonic Numbers； Generalized Harmonic Numbers； Abel’s Method on Summation by Parts
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。
Abstract: 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.
文章引用：王晓元, 孙艾莹. 含有高阶广义调和数的无穷级数恒等式[J]. 理论数学, 2024, 14(6): 178-192. https://doi.org/10.12677/pm.2024.146239

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