Several Characterizations of the Generalized 1-Parameter 3-Variable Hermite Polynomials

Shahid Ahmad Wani (), Khalil Hadi Hakami () and Hamad Zogan
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Shahid Ahmad Wani: Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, India
Khalil Hadi Hakami: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
Hamad Zogan: Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia

Mathematics, 2024, vol. 12, issue 16, 1-15

Abstract: This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite polynomials. These polynomials are characterized through generating functions and series definitions, elucidating their fundamental properties. Moreover, utilising a factorisation method, this study establishes recurrence relations, shift operators, and various differential equations, including differential, integro-differential, and partial differential equations.

Keywords: 1-parameter generalized Hermite polynomials; recurrence relations; differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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