Generating Relations of Generalized Hermite Polynomials by Weisner's Group Theoretic Method

Abstract

Abstract In this thesis we use Weisner’s group theoretic method to find different generating relations for generalized Hermite polynomials and functions. The cases that we discuss in this work include, Hermite two variables polynomial, Hermite matrix polynomial and function, and Hermite polynomial associated with parabolic cylinder. All the steps are shown in details starting from finding recurrence relations, commutative operator relations, the extended form of the groups generated by the operators, and ending with some new generalizations of well-known generating relations.