ON THE COMPLEX HERMITE POLYNOMIALS AND PARTIAL DIFFERENTIAL EQUATIONS

Abstract

ct. 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,
theNielsentypeformula,theadditionformulaforthecomplexHermitepolynomials
with ease. A multilinear generating function for the complex Hermite polynomials
is proved.