Some General Families of Generating Functions for the Laguerre Polynomials

The object of the present paper is to develop rather systematically some general families of bilinear, bilateral, or mixed multilateral generating functions for the classical Laguerre polynomials. Numerous straightforward consequences of some of the results considered here frequently appear in the literature, especially from the viewpoint of Lie groups and Lie algebras. It is also pointed out how the main generating functions can be suitably applied to derive numerous further results involving Laguerre polynomials and various other related polynomials.