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


Authors: Xia Zhou, Tianxin Cai and David M. Bradley
Journal: Proc. Amer. Math. Soc. 136 (2008), 2689-2698
MSC (2000): Primary 11M41; Secondary 11M06, 05A30, 33E20, 30B50
DOI: https://doi.org/10.1090/S0002-9939-08-09208-3
Published electronically: April 8, 2008
MathSciNet review: 2399030
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Xia Zhou
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Email: xiazhou0821@hotmail.com

Tianxin Cai
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Email: txcai@mail.hz.zj.cn

David M. Bradley
Affiliation: Department of Mathematics and Statistics, University of Maine, 5752 Neville Hall, Orono, Maine 04469-5752
Email: bradley@math.umaine.edu, dbradley@member.ams.org

DOI: https://doi.org/10.1090/S0002-9939-08-09208-3
Keywords: Tornheim's double series, alternating Euler sums, multiple harmonic series, multiple zeta values, $q$-analog, $q$-series.
Received by editor(s): January 19, 2007
Received by editor(s) in revised form: April 25, 2007
Published electronically: April 8, 2008
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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