Generalized $q$-Hermite Polynomials and the $q$-Dunkl Heat Equation

摘要

Two classes of generalized discrete q-Hermite polynomials are con- structed. Several properties of these polynomials, and an explicit relations con- necting them with little qg-Laguerre and q-Laguerre polynomials are obtained. A relationship with the g-Dunkl heat polynomials and the q-Dunkl associated functions are established.