Generalized Hermite polynomials in the description of multi-index Bessel functions

The Hermite polynomials represent a powerful tool to investigate the properties of many families of Special Functions. We discuss a special class of polynomials, recognized as Hermite polynomials, which present a flexible form to describe the two-index, one-variable Bessel functions. By using the generating function method, we will obtain some relations involving this class of Hermite polynomials and we can also compare them with the Humbert polynomials and functions.