The theory of generalized Bessel functions has found significant applications in the analysis of radiation phenomena, associated with charges moving in magnetic devices. In this paper we exploit the monomiality principle to discuss the theory of two-variable Laguerre polynomials and introduce the associated Laguerre-Bessel functions. We study their properties (addition and multiplication theorems, generating function, recurrence relations and so on) and discuss the link with the ordinary case. The usefulness of the obtained results to treat problems relevant to the paraxial propagation of electromagnetic waves is also discussed.
All Science Journal Classification (ASJC) codes
Dattoli, G., Torre, A., & Mancho, A. M. (2000). The generalized Laguerre polynomials, the associated Bessel functions and application to propagation problems. Radiation Physics and Chemistry, 59(3), 229 - 237. https://doi.org/10.1016/S0969-806X(00)00273-5