Open AccessOn the complex Hermite polynomials
Author(s) -
Zhi-Guo Liu
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2002409l
Subject(s) - mathematics , hermite polynomials , classical orthogonal polynomials , cubic hermite spline , orthogonal polynomials , multilinear map , difference polynomials , pure mathematics , discrete orthogonal polynomials , wilson polynomials , hermite interpolation , poisson kernel , hermite spline , complex quadratic polynomial , algebra over a field , mathematical analysis , polynomial , statistics , nearest neighbor interpolation , linear interpolation , bilinear interpolation , smoothing spline , spline interpolation
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.