涉及调和数的组合恒等式

陈玉磊, 郭东威

doi:10.13371/j.cnki.chin.q.j.m.2024.03.008

数学季刊 >

2024 , Vol. 39 >Issue 3: 307 - 314

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.03.008

涉及调和数的组合恒等式

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1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China

CHEN Yu-lei (1989-), female, native of Zhoukou, Henan, lecturer of Zhoukou Normal University, engages in number theory and its applications; GUO Dong-wei (1987-), male, native of Kaifeng, Henan, doctoral student of Nanjing University of Science and Technology, engages in combinatorics, economics.

收稿日期: 2023-07-31

网络出版日期: 2024-09-30

基金资助

Supported by Zhoukou Normal University High-Level Talents Start-Up Funds Research Project (Grant No. ZKNUC2022007) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX24 0725).

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Combinatorial Identities Concerning Harmonic Numbers

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1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China

Received date: 2023-07-31

Online published: 2024-09-30

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摘要

In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived.

关键词： Harmonic numbers; Coefficients; Combinatorial identities

本文引用格式

陈玉磊, 郭东威 . 涉及调和数的组合恒等式[J]. 数学季刊, 2024 , 39(3) : 307 -314 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.008

Abstract

Key words： Harmonic numbers; Coefficients; Combinatorial identities

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