The Legendre Polynomials as a Basis for Bessel Functions

By using the concepts and the formalism of the Monomiality Principle, we introduce a generalization of Bessel functions.The starting point is represented by Legendre polynomials, presented as particular case of generalized Laguerre polynomials of two variables.From the well known properties of the ordinary Bessel functions, we derive similar relations for this family of Legendre-Bessel functions, in particular, by exploiting the monomiality properties of Legendre polynomials, we discuss some differential rules of this family of generalized Bessel functions.