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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Komori, Yasushi Matsumoto, Kohji and Tsumura, Hirofumi 2015. Infinite series involving hyperbolic functions. Lithuanian Mathematical Journal, Vol. 55, Issue. 1, p. 102.
    Zaharescu, Alexandru and Zaki, Mohammad 2010. On the singularities of multiple L-functions. Central European Journal of Mathematics, Vol. 8, Issue. 2, p. 289.
    Tsumura, Hirofumi 2006. On some functional relations between Mordell–Tornheim double L-functions and Dirichlet L-functions. Journal of Number Theory, Vol. 120, Issue. 1, p. 161.
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Certain functional relations for the double harmonic series related to the double Euler numbers

  • Hirofumi Tsumura (a1)
Abstract

In this paper, we give certain analytic functional relations for the double harmonic series related to the double Euler numbers. These can be regarded as continuous generalizations of the known discrete relations obtained by the author recently.

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COPYRIGHT: © Australian Mathematical Society 2005
References
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[1]Dilcher, K., Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Mem. Amer. Math. Soc. 386 (Amer. Math. Soc., Providence, RI, 1988).
[2]Huard, J. G., Williams, K. S. and Nan-Yue, Z., ‘On Tornheim's double series’, Acta Arith. 75 (1996), 105–117.
[3]Matsumoto, K., ‘On Mordell-Tornheim and other multiple zeta-functions’, in: Proceedings of the Session in analytic number theory and Diophantine equations. Bonn, January-June 2002 (eds. Heath-Brown, D. R. and Moroz, B. Z.), Bonner Mathematische Schriften 360 (Bonn, 2003) pp. 17.
[4]Mordell, L. J., ‘On the evaluation of some multiple series’, J. London Math. Soc. 33 (1958), 368–371.
[5]Subbarao, M. V. and Sitaramachandrarao, R., ‘On some infinite series of L. J. Mordell and their analogues’, Pacific J. Math. 119 (1985), 245–255.
[6]Tornheim, L., ‘Harmonic double series’, Amer. J. Math. 72 (1950), 303–314.
[7]Tsumura, H., ‘On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function’, preprint.
[8]Tsumura, H., ‘On some combinatorial relations for Tornheim's double series’, Acta Arith. 105 (2002), 239–252.
[9]Tsumura, H., ‘On alternating analogues of Tornheim's double series’, Proc. Amer. Math. Soc. 131 (2003), 3633–3641.
[10]Tsumura, H., ‘Multiple harmonic series related to multiple Euler numbers’, J. Number Theory 106 (2004), 155–168.
[11]Washington, L. C., Introduction to the cyclotomic fields, 2nd edition (Springer, New York, 1997).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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