Some Families of Differential Equations Associated with Multivariate Hermite Polynomials-Reference-Cited by-同舟云学术

Some Families of Differential Equations Associated with Multivariate Hermite Polynomials

Published:2023-05-08 Issue:5 Volume:7 Page:390
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Alkahtani Badr Saad T.¹^ORCID,Alazman Ibtehal²^ORCID,Wani Shahid Ahmad³^ORCID

Affiliation:

1. Department of Mathematics, College of Science, King Saud University, Riyadh 11989, Saudi Arabia

2. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia

3. Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, India

Abstract

In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using the factorization approach. Families of differential equations, including differential, integro–differential, and partial differential equations, are obtained using these operators. The Volterra integral for these polynomials is also discovered.

Funder

King Saud University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/5/390/pdf

Reference16 articles.

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2. Appell, P., and Kampé de Fériet, J. (1926). Fonctions hypergéométriques et hypersphériques: Polynômes d’ Hermite, Gauthier-Villars.

3. Summation formulae of special functions and multivariable Hermite polynomials;Dattoli;Nuovo Cim. Soc. Ital. Fis.,2004