# 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)
Department of Mathematics
Journal
Integral Transforms and Special Functions
Volume
27
Pages
937-955
No. of pages
19
ISSN
1065-2469
DOI
https://doi.org/https://doi-org.uaccess.univie.ac.at/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