Some Families of Differential Equations Associated with Multivariate Hermite Polynomials

Author:

Alkahtani Badr Saad T.1ORCID,Alazman Ibtehal2ORCID,Wani Shahid Ahmad3ORCID

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

Reference16 articles.

1. The factorization method;Infeld;Rev. Mod. Phys.,1951

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

4. Differential equation of Appell polynomials via factorization method;He;J. Comput. Appl. Math.,2002

5. Multidimensional extension of the Bernoulli and Appell polynomials;Bretti;Taiwan. J. Math.,2004

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