Hankel determinants of generalized q-exponential polynomials

TL;DR

This paper explores two q-analogues of generalized exponential polynomials and computes their Hankel determinants, extending recent work on exponential polynomial generalizations.

Contribution

It introduces two new q-analogues of exponential polynomials and calculates their Hankel determinants, providing new insights into their algebraic properties.

Findings

Computed Hankel determinants for the q-analogues

Extended understanding of exponential polynomial generalizations

Provided explicit formulas for determinants

Abstract

Recently I. Mezo studied a simple but interesting generalization of the exponential polynomials. In this note I consider two q-analogues of these polynomials and compute their Hankel determinants.