广义调和数与广义调和函数的若干恒等式

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2022-12-30 DOI:10.1515/dema-2022-0229

Dae San Kim, H. Kim, Taekyun Kim

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引用次数: 2

摘要

调和数和广义调和数经常出现在许多不同的领域，如组合问题、解析数论中许多涉及特殊函数的表达式、算法分析等。本文的目的是利用初等方法，从函数F n (x)=B (x+1,n+1)， (n=0,1,2，…){F＿n}{}\left (x)=B \left (x+1,n+1)， \left (n=0,1,2, \ldots)中导出一些涉及广义调和数和广义调和函数的恒等式。例如，我们证明了Hurwitz ζ函数ζ (x+1,r) \zeta\left (x+1,r)和r !r\!用这些数和函数表示，对于每个r=2,3,4,5 r=2,3,4,5。

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Some identities on generalized harmonic numbers and generalized harmonic functions

Abstract The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this article is to derive some identities involving generalized harmonic numbers and generalized harmonic functions from the beta functions F n ( x ) = B ( x + 1 , n + 1 ) , ( n = 0 , 1 , 2 , … ) {F}_{n}\left(x)=B\left(x+1,n+1),\left(n=0,1,2,\ldots ) using elementary methods. For instance, we show that the Hurwitz zeta function ζ ( x + 1 , r ) \zeta \left(x+1,r) and r ! r\! are expressed in terms of those numbers and functions, for every r = 2 , 3 , 4 , 5 r=2,3,4,5 .

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.