GENERALIZED BESSEL FUNCTIONS IN TERMS OF GENERALIZED HERMITE POLYNOMIALS

The Hermite polynomials represent a powerful tool to investigate the properties of many families of Special Functions. We present some relevant results where the generalized Hermite polynomials of Kamp´e de F´eriet type, simplify the definitions and the operational properties of the two-variable, generalized Bessel functions and their modified. We also 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 these classes of Hermite polynomials and we can also compare them with the Humbert polynomials and functions.