Signed $q$-analogs of Tornheim's double series

DOI10.1090/S0002-9939-08-09208-3zbMath1204.11150arXiv0705.0698MaRDI QIDQ3518223

Tian Xin Cai, Xia Zhou, David M. Bradley

Publication date: 7 August 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.0698

zbMATH Keywords

\(q\)-seriesmultiple zeta values\(q\)-analogmultiple harmonic seriesTornheim's double seriesalternating Euler sums

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) (zeta (s)) and (L(s, chi)) (11M06) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Other functions defined by series and integrals (33E20) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (10)

Computation and structure of character polylogarithms with applications to character Mordell–Tornheim–Witten sums ⋮ On the summability of bivariate rational functions ⋮ A simple proof of the functional relation for the Lerch type Tornheim double zeta function ⋮ On functional relations for the alternating analogues of Tornheim's double zeta function ⋮ Euler sums of generalized harmonic numbers and connected extensions ⋮ Evaluation of Tornheim's type of double series ⋮ Analytic Continuations of Character and Alternating Tornheim Zeta Functions ⋮ Alternating double Euler sums, hypergeometric identities and a theorem of Zagier ⋮ Remarks on double zeta values of level 2 ⋮ Double Lerch value relations and functional relations for Witten zeta functions

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