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Infinite series involving hyperbolic functions

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Abstract

In the first part of this paper, we summarize our previous results on infinite series involving the hyperbolic sine function, especially, with a focus on the hyperbolic sine analogue of Eisenstein series. Those are based on the classical results given by Cauchy, Mellin, and Kronecker. In the second part, we give new formulas for some infinite series involving the hyperbolic cosine function.

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Authors and Affiliations

  1. Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan

    Yasushi Komori

  2. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

    Kohji Matsumoto

  3. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan

    Hirofumi Tsumura

Authors
  1. Yasushi Komori
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  2. Kohji Matsumoto
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  3. Hirofumi Tsumura
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Correspondence to Yasushi Komori.

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Komori, Y., Matsumoto, K. & Tsumura, H. Infinite series involving hyperbolic functions. Lith Math J 55, 102–118 (2015). https://doi.org/10.1007/s10986-015-9268-x

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  • DOI: https://doi.org/10.1007/s10986-015-9268-x

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