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February, 2021 Homogeneous $q$-difference Equations and Generating Functions for the Generalized 2D-Hermite Polynomials
Zeya Jia
Taiwanese J. Math. 25(1): 45-63 (February, 2021). DOI: 10.11650/tjm/200804

Abstract

In this paper, we deduce several types of generating functions for $q$-2D Hermite polynomial by the method of homogeneous $q$-difference equations. Besides, we deduce a multilinear generating function for $q$-2D Hermite polynomials as a generalization of Andrew's result. Moreover, we build a transformation identity involving the generalized $q$-2D Hermite polynomials by the method of homogeneous $q$-difference equations. As an application, we give a transformation identity involving $D_{q}(m,n)$ and $D_{q}^{*}(m,n)$.

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Zeya Jia. "Homogeneous $q$-difference Equations and Generating Functions for the Generalized 2D-Hermite Polynomials." Taiwanese J. Math. 25 (1) 45 - 63, February, 2021. https://doi.org/10.11650/tjm/200804

Information

Received: 20 April 2019; Revised: 2 August 2020; Accepted: 16 August 2020; Published: February, 2021
First available in Project Euclid: 24 August 2020

Digital Object Identifier: 10.11650/tjm/200804

Subjects:
Primary: 11B65, 11B83, 33C50, ‎33D45, 39A13

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 1 • February, 2021
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