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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On alternating analogues of Tornheim's double series


Author: Hirofumi Tsumura
Journal: Proc. Amer. Math. Soc. 131 (2003), 3633-3641
MSC (2000): Primary 11M06; Secondary 30B99, 33E20, 40A05, 40B05
Published electronically: July 9, 2003
MathSciNet review: 1998168
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Abstract: In this paper, we give some evaluation formulas for alternating analogues of Tornheim's double series. These can be regarded as alternating analogues of Mordell's formulas. This gives a partial answer to the problem posed by Subbarao-Sitaramachandrarao.


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Additional Information

Hirofumi Tsumura
Affiliation: Department of Management Informatics, Tokyo Metropolitan College, Akishima, Tokyo 196-8540 Japan
Email: tsumura@tmca.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07186-7
PII: S 0002-9939(03)07186-7
Keywords: Tornheim's double series, Euler numbers, Riemann's zeta function, uniformly convergent series
Received by editor(s): March 22, 2002
Received by editor(s) in revised form: May 28, 2002
Published electronically: July 9, 2003
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2003 American Mathematical Society