Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Symmetric Tornheim double zeta functions

Symmetric Tornheim double zeta functions Let s,t,u∈C\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s,t,u \in {{\mathbb {C}}}$$\end{document} and T(s, t, u) be the Tornheim double zeta function. In this paper, we investigate some properties of symmetric Tornheim double zeta functions which can be regarded as a desingularization of the Tornheim double zeta function. As a corollary, we give explicit evaluation formulas or rapidly convergent series representations for T(s, t, u) in terms of series of the gamma function and the Riemann zeta function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

Loading next page...
 
/lp/springer-journals/symmetric-tornheim-double-zeta-functions-2xT0qsF0dm
Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2021
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-021-00232-4
Publisher site
See Article on Publisher Site

Abstract

Let s,t,u∈C\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s,t,u \in {{\mathbb {C}}}$$\end{document} and T(s, t, u) be the Tornheim double zeta function. In this paper, we investigate some properties of symmetric Tornheim double zeta functions which can be regarded as a desingularization of the Tornheim double zeta function. As a corollary, we give explicit evaluation formulas or rapidly convergent series representations for T(s, t, u) in terms of series of the gamma function and the Riemann zeta function.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Apr 1, 2021

Keywords: Tornheim double zeta function; Desingularization; Rapidly convergent series representation; Primary 11M32

References