A class of polynomials defined by generalized Rodrigues’ formula

Abstract

The present paper incorporates a systematic study of linear, bilinear and bilateral generating functions, pure as well as mixed recurrence relations, and the differential equations associated with the class of polynomials {G α (x, r, p, k)|n=0, 1, 2, ... }, defined by (1.3) below, which evidently provides an elegant generalization of the various recent extensions of the classical Hermite and Laguerre polynomials.