On a class of two-index real Hermite polynomials

TL;DR

This paper introduces a new class of doubly indexed real Hermite polynomials and explores their mathematical properties such as recurrence relations, addition formulas, generating functions, and identities.

Contribution

The paper presents a novel class of two-index real Hermite polynomials and derives their fundamental properties, expanding the theoretical framework of Hermite polynomial families.

Findings

Derived recurrence relations for the new polynomials

Established Runge's addition formula for the class

Presented the generating function and Nielsen's identity

Abstract

We introduce a class of doubly indexed real Hermite polynomials and we deal with their related properties like the associated recurrence formulae, Runge's addition formula, generating function and Nielsen's identity.