English

Signed q-Analogs of Tornheim's Double Series

Number Theory 2008-07-18 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.0705.0698,
  title  = {Signed q-Analogs of Tornheim's Double Series},
  author = {Xia Zhou and Tianxin Cai and David M. Bradley},
  journal= {arXiv preprint arXiv:0705.0698},
  year   = {2008}
}

Comments

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