Theory of multiindex multivariable Bessel functions and Hermite polynomials

Abstract

We discuss the theory of multivariable multiindex Bessel functions (B.F.) and Hermite polynomials (H.P.) using the generating function method. We derive addition and multiplication theorems and discuss how generalized H.P. can be exploited as a useful complement to the theory of B.F.. We also discuss the importance of the Poisson-Charlier polynomials in the context of multiindex special functions.

Keywords

• Hermite polynomials
• Appel-Kampé de Fériet polynomials
• Bessel functions
• Charlier-Poisson polynomials
• Anger functions