Evaluations of Series of Hyperbolic Functions

TL;DR

This paper evaluates specific series of hyperbolic functions using Jacobi elliptic functions and introduces new functions to characterize unsolvable series classes.

Contribution

It provides new evaluations of hyperbolic series and defines novel functions for classifying unsolvable series.

Findings

Evaluations of hyperbolic function series using elliptic functions

Introduction of new functions for classifying series

Characterization of unsolvable series classes

Abstract

In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.