Summation formula for generalized discrete $q$-Hermite II polynomials

Abstract

In this paper, we provide a family of generalized discrete $q$-Hermite II polynomials denoted by ${\tilde{h}}_{n,\alpha }(x,y|q)$. An explicit relations connecting them with the $q$-Laguerre and Stieltjes-Wigert polynomials are obtained. Summation formula is derived by using different analytical means on their generating functions.

12 pages