Advancements in $ q $-Hermite-Appell polynomials: a three-dimensional exploration-Reference-Cited by-同舟云学术

Advancements in $ q $-Hermite-Appell polynomials: a three-dimensional exploration

Published:2024 Issue:10 Volume:9 Page:26799-26824
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zayed Mohra¹,Wani Shahid Ahmad²,Ramírez William³⁴,Cesarano Clemente⁴

Affiliation:

1. Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia

2. Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India

3. Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58, 55-66, Barranquilla 080002, Colombia

4. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, Rome 00186, Italy

Abstract

<p>In this research, we leverage various $ q $-calculus identities to introduce the notion of $ q $-Hermite-Appell polynomials involving three variables, elucidating their formalism. We delve into numerous properties and unveil novel findings regarding these $ q $-Hermite-Appell polynomials, encompassing their generating function, series representation, summation equations, recurrence relations, $ q $-differential formula, and operational principles. Our investigation sheds light on the intricate nature of these polynomials, elucidating their behavior and facilitating deeper understanding within the realm of $ q $-calculus.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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