Signed $q$-analogs of Tornheim’s double series
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- by Xia Zhou, Tianxin Cai and David M. Bradley
- Proc. Amer. Math. Soc. 136 (2008), 2689-2698
- DOI: https://doi.org/10.1090/S0002-9939-08-09208-3
- Published electronically: April 8, 2008
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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.References
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Bibliographic 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
- MR Author ID: 329306
- ORCID: 0000-0003-2952-2366
- Email: bradley@math.umaine.edu, dbradley@member.ams.org
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2399030