2017/07/27 by Zhiguo Liu, Liu, Zhi-Guo
Mathematics · Physics and Astronomy · #32A05 #32A10 #33C45 #35C11 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1707.08708
openalex publication_date 2017/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.