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

## TL;DR

This paper introduces a new family of generalized discrete q-Hermite II polynomials, establishes their relations with other q-polynomials, and derives a summation formula using generating functions.

## Contribution

It presents a novel family of generalized discrete q-Hermite II polynomials and connects them with q-Laguerre and Stieltjes-Wigert polynomials, along with a new summation formula.

## Key findings

- Explicit relations with q-Laguerre and Stieltjes-Wigert polynomials
- Derived summation formula for the polynomials
- Enhanced understanding of their generating functions

## 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.