Evaluations of Series Related to Jacobi Elliptic Functions

TL;DR

This paper evaluates specific hyperbolic series using Jacobi elliptic functions and introduces new functions to characterize series that are not solvable.

Contribution

It provides new evaluations of hyperbolic series and defines novel functions for classifying unsolvable series within the Jacobi elliptic functions framework.

Findings

Evaluations of certain hyperbolic series using Jacobi elliptic functions.

Introduction of new functions to characterize non-solvable series.

Enhanced understanding of series solvability in elliptic functions context.

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.