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Evaluation formulas for Tornheim's type of alternating double series

Author(s): Hirofumi Tsumura.
Journal: Math. Comp. 73 (2004), 251-258.
MSC (2000): Primary 11M06; Secondary 30B99, 33E20, 40A05, 40B05
Posted: July 14, 2003
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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:

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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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