Some evaluation of q-analogues of Euler sums

Author(s)
Ce Xu, Mingyu Zhang, Weixia Zhu
Abstract

In this paper, we discuss the analytic representations of q-Euler sums which involve q-harmonic numbers through q-polylogarithms, either linearly or nonlinearly, and give explicit formulae for several classes of q-Euler sums in terms of q-polylogarithms and q-special functions. Furthermore, we develop new closed form representations of sums of quadratic and cubic parametric q-Euler sums. Finally, we can find that the q-Euler sums are reducible to the classical Euler sums when q approaches 1.

Organisation(s)
Department of Mathematics
Journal
Monatshefte für Mathematik
Volume
182
Pages
957-975
No. of pages
19
ISSN
0026-9255
DOI
https://doi.org/10.1007/s00605-016-0915-z
Publication date
04-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
101025 Number theory, 101002 Analysis
Keywords
ASJC Scopus subject areas
Mathematics(all)
Portal url
https://ucris.univie.ac.at/portal/en/publications/some-evaluation-of-qanalogues-of-euler-sums(59abcaf9-2763-4b1f-927b-184afe18934d).html