Two-dimensional $(p,q)$-heat polynomials of Gould--Hopper type
Abstract
We introduce a new class of holomorphic polynomials extending the classical Gould--Hopper to two complex variables. The considered polynomials include the -D and -D holomorphic and polyanalytic It\^o--Hermite polynomials as particular cases. We emphasize studying their operational representation, various generating functions, and recurrence relations. We also establish some special identities including multiplication and addition formulas of Runge type, as well as the Nielson type formulas. Higher-order partial differential equations are analyzed and the connection to Gould-Hopper polynomials and hypergeometric functions are investigated.
Keywords
Cite
@article{arxiv.1907.10744,
title = {Two-dimensional $(p,q)$-heat polynomials of Gould--Hopper type},
author = {Allal Ghanmi and Khalil Lamsaf},
journal= {arXiv preprint arXiv:1907.10744},
year = {2021}
}
Comments
14 pages, This is an improved version of the previous one entitled "A Unified generalization of real, Gould--Hopper, 1-d and 2-d holomorphic, and polyanalytic Hermite Polynomials"