Generating Functions for Laguerre Polynomials: New Identities for Lacunary Series

TL;DR

This paper introduces new generating function identities for Laguerre polynomials, including lacunary series and exponential forms, expanding the mathematical tools available for their analysis.

Contribution

It provides novel identities involving lacunary and exponential generating functions for standard and associated Laguerre polynomials.

Findings

Derived double- and triple-lacunary generating functions

Established new identities for exponential generating functions

Extended the theory of Laguerre polynomial series

Abstract

We present a number of identities involving standard and associated Laguerre polynomials. They include double-, and triple-lacunary, ordinary and exponential generating functions of certain classes of Laguerre polynomials.