Journal of East China Normal University(Natural Science) >

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

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

Mathematics

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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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

Cite this article

Qinglun YAN , Zhaofen WANG , Juan MI . Finite sums in higher order powers of shifted-harmonic numbers[J]. Journal of East China Normal University(Natural Science), 2021 , 2021(6) : 24 -32 . DOI: 10.3969/j.issn.1000-5641.2021.06.003

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