SOME SPECIAL CLASSES OF BESSEL FUNCTIONS AND MODIFIED HUMBERT FUNCTIONS

Bessel functions represent an important chapter of mathematical analysis and have been widely used in many applications. Considered the flexibility and richness of their properties, Bessel functions have been generalized in various ways. We will discuss some relevant properties related to the two-index Bessel functions and we will exposed some differential results regarding the particular class of the one-parameter, two-variable, generalized Bessel functions. Further, by starting from a particular class of functions, which derives from those introduced by P. Humbert in 1930 and called Bessel functions of third kind, we will introduce a family of modified Humbert functions and we will show some results related to the multiplication and addition formulae, which can be derived by using the techniques of generating function and by following the structure of similar properties satisfied by generalized Bessel functions.