Hermite and Laguerre polynomials with complex matrix arguments Original Research Article

This paper defines and discusses the complex Hermite and Laguerre polynomials associated with the complex matrix-variate normal and Wishart distributions, respectively. Various properties of these polynomials are investigated, including generating functions, Rodrigues formulae (differential and integral versions), and series expressions. These polynomials are also discussed from the viewpoint of the multivariate complex Meixner distributions. We present applications in asymptotic distribution theory on the complex Stiefel manifold. The theory of complex zonal polynomials is of great use in the derivations.