Infinite series involving hyperbolic functions

TL;DR

This paper reviews previous findings on infinite series with hyperbolic sine functions and introduces new formulas for series involving hyperbolic cosine functions, expanding the mathematical understanding of these series.

Contribution

It provides a comprehensive summary of earlier results and presents novel formulas for hyperbolic cosine series, extending classical hyperbolic series analysis.

Findings

New formulas for hyperbolic cosine series derived.

Extended classical results on hyperbolic sine series.

Connections to Eisenstein series and classical analysis.

Abstract

In the former 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 latter part, we give new formulas for some infinite series involving the hyperbolic cosine function.