数学季刊 ›› 2024, Vol. 39 ›› Issue (3): 307-314.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.008

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涉及调和数的组合恒等式

  

  1. 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
  • 收稿日期:2023-07-31 出版日期:2024-09-30 发布日期:2024-09-30
  • 通讯作者: GUO Dong-wei (1987-), male, native of Kaifeng, Henan, doctoral student of Nanjing University of Science and Technology, engages in combinatorics, economics. E-mail:guo.dongwei@njust.edu.cn
  • 作者简介: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.
  • 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).

Combinatorial Identities Concerning Harmonic Numbers

  1. 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:2023-07-31 Online:2024-09-30 Published:2024-09-30
  • Contact: GUO Dong-wei (1987-), male, native of Kaifeng, Henan, doctoral student of Nanjing University of Science and Technology, engages in combinatorics, economics. E-mail:guo.dongwei@njust.edu.cn
  • About author: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.
  • Supported by:
    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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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

Abstract: 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.

Key words:  Harmonic numbers, Coefficients, Combinatorial identities

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