华东师范大学学报（自然科学版） >

2021 , Vol. 2021 >Issue 6: 24 - 32

DOI: https://doi.org/10.3969/j.issn.1000-5641.2021.06.003

数学

高阶shifted调和数的有限求和

  • 闫庆伦 ,
  • 王照芬 ,
  • 米娟
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  • 南京邮电大学 理学院, 南京　210023
闫庆伦, 男, 副教授, 硕士生导师, 研究方向为组合数学. E-mail: yanqinglun@njupt.edu.cn

收稿日期: 2020-08-19

  网络出版日期: 2021-11-26

基金资助

南京邮电大学科研项目(NY218061)

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Finite sums in higher order powers of shifted-harmonic numbers

  • Qinglun YAN ,
  • Zhaofen WANG ,
  • Juan MI
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  • College of Science, Nanjing University of Posts and Telecommunications, Nanjing　210023, China

Received date: 2020-08-19

  Online published: 2021-11-26

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摘要

在本文中, 我们利用部分分式法等方法研究了一组关于Euler型求和的组合恒等式, 计算了有关高阶shifted调和数与二项式系数的倒数的乘积的有限求和形式. 通过对参数取特殊值, 可以得到许多有意义的恒等式.

关键词： 调和数; 二项式系数; 部分分式法

本文引用格式

闫庆伦 , 王照芬 , 米娟 . 高阶shifted调和数的有限求和[J]. 华东师范大学学报（自然科学版）, 2021 , 2021(6) : 24 -32 . DOI: 10.3969/j.issn.1000-5641.2021.06.003

Abstract

In this article, using methods such as the partial fraction method, we study a set of combined identities for an Euler-type summation. We calculate, furthermore, the finite summation form of the product of the high order shifted-harmonic number and the reciprocal of the binomial coefficient. By using special values for the parameters, interesting identities can be obtained.

Key words： harmonic numbers; binomial coefficient; the partial fraction method

参考文献

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