Comments on "New generating relations for products of two Laguerre polynomials"

TL;DR

This paper corrects errors in Exton's previously published double generating relations for Laguerre polynomials, providing accurate formulas and expanding their connections to elementary functions, Bessel functions, and Hermite polynomials.

Contribution

It offers corrected and clarified double generating relations for Laguerre polynomials derived from a two-dimensional series transform.

Findings

Corrected formulas for double generating relations

Expanded connections to elementary functions and special functions

Clarified previous errors in Exton's results

Abstract

By utilizing a two-dimensional extension of a very general series transform given by Bailey, Exton [Indian J. pure appl. Math. 24 (6) (1993), 401-408] deduced a very general double generating relation of a product of a pair of Laguerre polynomials and obtained a number of useful relations with elementary functions, Bessel functions, Hermite polynomials and single series expansions of pairs of Laguerre polynomials. Unfortunately, some of the results given by Exon contain errors and thus this is the aim of this short note to provide the corrected form of these results.