A note on a series containing the Laguerre polynomials

TL;DR

This paper derives new summation formulas for series involving Laguerre polynomials using generalized hypergeometric functions, offering simpler alternatives to existing results.

Contribution

It introduces novel summation expressions for Laguerre polynomial series in terms of hypergeometric functions, simplifying previous complex formulas.

Findings

Derived new series summation formulas involving Laguerre polynomials.

Expressed these sums in terms of generalized hypergeometric functions.

Provided simpler alternatives to existing formulas in the literature.

Abstract

Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently obtained in the literature.