Infinite series involving hyperbolic functions

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.