Some Families of Differential Equations Associated with Multivariate Hermite Polynomials

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.

Keywords

• Hermite polynomials
• recurrence relation
• shift operators
• differential equations
• integral equation