GENERALIZED BESSEL-FUNCTIONS AND KAPTEYN SERIES

Kapteyn series are introduced for generalized Bessel functions in full analogy with ordinary Bessel functions. Apart from the relevance that Kapteyn series have in astronomical problems and in electromagnetic r adiation theory, interest in this type of series is justified by the p ossibility of expanding analytic functions of a complex variable in se ries of Bessel functions with specific features. Accordingly, in this paper, it is shown that it is possible to obtain expansions of m-varia ble analytic functions in series of GBF's, which reproduce the structu re of Kapteyn series of ordinary Bessel functions. The possible field of applications is also suggested.