Kuba, Markus On evaluations of infinite double sums and Tornheim’s double series. (English) Zbl 1196.11122 Sémin. Lothar. Comb. 58, B58d, 11 p. (2007). Summary: We consider generalizations of a sum, which was recently analyzed by R. Pemantle and C. Schneider [Am. Math. Mon. 114, No. 4, 344–350 (2007; Zbl 1226.11134)] using the computer software Sigma, and later also by A. Panholzer and R. Prodinger [Sémin. Lothar. Comb. 55, B55a, 3 p., electronic only (2005; Zbl 1088.11066)]. Our generalizations include Tornheim’s double series as a special case. We also consider alternating analogs of Tornheim’s series. For Tornheim’s double series and its alternating counterparts we provide short proofs for evaluation formulas, which recently appeared in the literature. We introduce finite Tornheim double sums and alternating analogs, and provide relations to finite multiple zeta functions, similarly to the infinite case. Besides, we discuss the evaluation of another double series, which also generalizes Tornheim’s double series. Cited in 3 Documents MSC: 11M41 Other Dirichlet series and zeta functions 40B05 Multiple sequences and series 11Y60 Evaluation of number-theoretic constants Keywords:Tornheim’s double series; Euler sums; alternating double series Citations:Zbl 1088.11066; Zbl 1226.11134 PDFBibTeX XMLCite \textit{M. Kuba}, Sémin. Lothar. Comb. 58, B58d, 11 p. (2007; Zbl 1196.11122) Full Text: EuDML EMIS