On a Method for Solving Infinite Series

TL;DR

This paper introduces a novel method for solving infinite series in closed form by applying inverse and forward Laplace transforms, extending it through parametrization and additional transforms for greater flexibility.

Contribution

It presents a new approach using Laplace transforms to solve infinite series, including parametrization and multiple transforms for enhanced solution techniques.

Findings

Provides a method to solve infinite series in closed form

Extends the method with parametrization and additional Laplace transforms

Offers more options for solving series through integral transforms

Abstract

This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace transform with respect to it will offer more options for solving a series.