Séminaire Lotharingien de Combinatoire, B58d (2008), 11 pp.
On Evaluations of Infinite Double Sums and Tornheim's Double Series
We consider generalizations of a sum, which was recently analyzed by
Pemantle and Schneider using the computer software Sigma,
and later also by Panholzer and Prodinger. 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.
Received: June 29, 2007.
Accepted: January 6, 2008.
Final Version: March 18, 2008.
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