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

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