Signed q-Analogs of Tornheim's Double Series

Abstract

We introduce signed q-analogs of Tornheim's double series, and evaluate them in terms of double q-Euler sums. As a consequence, we provide explicit evaluations of signed and unsigned Tornheim double series, and correct some mistakes in the literature.

12 pages, AMSLaTeX. The multinomial notation introduced on page 3 just before Theorem 1 is insufficiently general in version 1, since it may happen that the upper number is negative. This is corrected in version 2, which allows for a negative or even complex upper argument

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Cited by in corpus (5)

• On Mordell-Tornheim sums and multiple zeta values
• On functional relations for the alternating analogues of Tornheim's double zeta function
• Simple proof of the functional relation for the Lerch type Tornheim double zeta function
• On the Summability of Bivariate Rational Functions
• Evaluation of Tornheim's type of double series