q-Bessel functions: the point of view of the generating function method

Abstract

We show that the generating function method allows a fairly straightforward understanding of the properties of q-Bessel functions. We analyze three different forms of cylindrical q-Bessel functions so far proposed, discuss their generating functions, the recurrence relations they satisfy, and the relevant addition and multiplication theorems. We also introduce q-Bessel functions of the I-type and touch on the possibility of considering q-Bessel functions with more than one variable, as well as q-Kampé de Fériét polynomials.

Keywords

• bessel functions
• generating functions
• q-polynomials