Some generating functions of the Laguerre and modified Laguerre polynomials

Abstract

Recently, by applying the familiar group-theoretic method of Louis Weisner (1899–1988), many authors proved various single- as well as multiple-series generating functions for certain modified Laguerre polynomials. The main object of the present sequel to these earlier works is to show how readily each of such generating functions can be derived from the corresponding known result for the classical Laguerre polynomials. Many general families of bilinear, bilateral, or mixed multilateral generating functions for the Laguerre (or modified Laguerre) and related polynomials, which are seemingly relevant to the present investigation, are also considered.