An extension of a series containing Laguerre polynomials

TL;DR

This paper derives new formulas for summing series involving Laguerre polynomials using hypergeometric functions, extending previous mathematical results in special functions.

Contribution

It provides generalized expressions for series involving Laguerre polynomials, expanding the mathematical tools available for their analysis.

Findings

Derived formulas for Laguerre polynomial series

Expressed results in terms of hypergeometric functions

Extended previous mathematical literature

Abstract

Expressions for the summation of the series involving the Laguerre polynomials \[S_m(\pm\nu, \pm p)\equiv e^{-x}\sum_{n=0}^\infty \frac{x^n\,L_n^{(\nu)}(x)}{(1\pm \nu\pm p)_n}\frac{(f+m)_n}{(f)_n}\] for any non-negative integers $m$ and $p$ are obtained in terms of generalized hypergeometric functions. These results extend previous work in the literature.