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. Starting from the two-index Bessel functions, we will discuss a particular class of functions which derives from those introduced by P. Humbert in 1930 and called Bessel functions of third kind. In particular, we will introduce a family of modified Humbert functions and will present some results related to the multiplication and addition formulae, which can be derived using the techniques of generating function and following the structure of similar properties satisfied by generalized Bessel functions.
A note on modified Humbert functions
CESARANO C
2015-01-01
Abstract
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. Starting from the two-index Bessel functions, we will discuss a particular class of functions which derives from those introduced by P. Humbert in 1930 and called Bessel functions of third kind. In particular, we will introduce a family of modified Humbert functions and will present some results related to the multiplication and addition formulae, which can be derived using the techniques of generating function and following the structure of similar properties satisfied by generalized Bessel functions.| File | Dimensione | Formato | |
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