Some evaluation of harmonic number sums
- Author(s)
- Ce Xu, Mingyu Zhang, Weixia Zhu
- Abstract
In this paper, by using the method of partial fraction decomposition and integral representations of series, we establish some expressions of series involving harmonic numbers and binomial coefficients in terms of zeta values and harmonic numbers. Furthermore, we can obtain some closed form representations of sums of products of quadratic (or cubic) harmonic numbers and reciprocal binomial coefficients, and some explicit evaluations are given as applications. The given representations are new.
- Organisation(s)
- External organisation(s)
- Xiamen University
- Journal
- Integral Transforms and Special Functions
- Volume
- 27
- Pages
- 937-955
- No. of pages
- 19
- ISSN
- 1065-2469
- DOI
- https://doi.org/10.1080/10652469.2016.1231675
- Publication date
- 12-2016
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101025 Number theory
- Keywords
- ASJC Scopus subject areas
- Analysis, Applied Mathematics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/some-evaluation-of-harmonic-number-sums(6b0f990a-1833-4e34-ab96-f315d1734d10).html