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

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 esta...

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Bibliographic Details
Published in:	Mathematics (Basel) Vol. 12; no. 16; p. 2459
Main Authors:	Wani, Shahid Ahmad, Hakami, Khalil Hadi, Zogan, Hamad
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-08-2024
Subjects:	1-parameter generalized Hermite polynomials Applied mathematics differential equations Fourier transforms Hermite polynomials Numerical analysis Operators (mathematics) Parameters Partial differential equations Polynomials Quantum physics recurrence relations Signal processing
Online Access:	Get full text
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Summary:	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.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math12162459