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.