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Evaluation formulas for Tornheim's type of alternating double series


Author: Hirofumi Tsumura
Journal: Math. Comp. 73 (2004), 251-258
MSC (2000): Primary 11M06; Secondary 30B99, 33E20, 40A05, 40B05
DOI: https://doi.org/10.1090/S0025-5718-03-01572-2
Published electronically: July 14, 2003
MathSciNet review: 2034120
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.


References [Enhancements On Off] (What's this?)

  • 1. K. Dilcher, Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Memoirs of A.M.S. 386 (1988). MR 89h:30005
  • 2. J. G. Huard, K. S. Williams and Z. Nan-Yue, On Tornheim's double series, Acta Arith. 75-2 (1996), 105-117. MR 97f:11073
  • 3. M. V. Subbarao and R. Sitaramachandrarao, On some infinite series of L. J. Mordell and their analogues, Pacific J. Math., 119 (1985), 245-255. MR 87c:11091
  • 4. L. Tornheim, Harmonic double series, Amer. J. Math. 72 (1950), 303-314. MR 11:654a
  • 5. H. Tsumura, On some combinatorial relations for Tornheim's double series, Acta Arith., 105 (2002), 239-252.
  • 6. H. Tsumura, On alternating analogues of Tornheim's double series, Proc. Amer. Math. Soc., 131 (2003), 3633-3641.

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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: https://doi.org/10.1090/S0025-5718-03-01572-2
Keywords: Tornheim's double series, Euler polynomials, Riemann's zeta function, uniformly convergent series
Received by editor(s): April 11, 2002
Published electronically: July 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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