Some generating functions for the Laguerre and related polynomials

摘要

The authors investigate (and present generalizations of) several generating functions of the classical Laguerre and related polynomials. One of these generating functions was recently rederived probabilistically by Lee [P.-A. Lee, Bull. Inst. Math. Acad. Sinica 25 (1997) 151–154], who made use of the theory of a class of probability distributions known as the non-central negative binomial distribution. Basic (or q-) extensions of the main series identities are also considered.