On the complex Hermite polynomials and partial differential equations
Complex Variables
2019-05-10 v2
Abstract
In this paper we use a set of partial differential equations to prove an expansion theorem for multiple complex Hermite polynomials. This expansion theorem allows us to develop a systematic and completely new approach to the complex Hermite polynomials. Using this expansion, we derive the Poisson Kernel, the Nielsen type formula, the addition formula for the complex Hermite polynomials with ease. A multilinear generating function for the complex Hermite polynomials is proved.
Keywords
Cite
@article{arxiv.1707.08708,
title = {On the complex Hermite polynomials and partial differential equations},
author = {Zhi-Guo Liu},
journal= {arXiv preprint arXiv:1707.08708},
year = {2019}
}