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On alternating analogues of Tornheim's double series
Author(s):
Hirofumi
Tsumura
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3633-3641.
MSC (2000):
Primary 11M06;
Secondary 30B99, 33E20, 40A05, 40B05
Posted:
July 9, 2003
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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.
References:
- 1.
- K. Dilcher, Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Memoirs of Amer. Math. Soc. 73, No. 386 (1988). MR 89h:30005
- 2.
- J. G. Huard, K. S. Williams and Nan-Yue Zhang, On Tornheim's double series, Acta Arith. 75-2 (1996), 105-117. MR 97f:11073
- 3.
- L. J. Mordell, On the evaluation of some multiple series, J. London Math. Soc. 33 (1958), 368-371. MR 20:6615
- 4.
- M. V. Subbarao and R. Sitaramachandra Rao, On some infinite series of L. J. Mordell and their analogues, Pacific J. Math. 119 (1985), 245-255. MR 87c:11091
- 5.
- L. Tornheim, Harmonic double series, Amer. J. Math. 72 (1950), 303-314. MR 11:654a
- 6.
- H. Tsumura, On some combinatorial relations for Tornheim's double series, Acta Arith. 105 (2002), 239-252.
- 7.
- H. Tsumura, On Tornheim's type of double harmonic series, submitted.
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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:
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
Posted:
July 9, 2003
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2003,
American Mathematical Society
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