Generalized Bessel Functions and Their Use in Bremsstrahlung and Multi-Photon Processes

The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study electro-magnetic processes presented. We consider cases emission bremsstrahlung radiation by ultra-relativistic electrons linearly polarized undulators, including also exotic configurations, aimed at enhancing harmonic content emitted radiation. analysis eventually extended generalization FEL pendulum equation treat Free Electron Laser operating with multi-harmonic undulators. paper aims picking out those elements supporting usefulness elaboration underlying spectral properties relativistic charges, along relevant flexibility accounting for a large variety apparently uncorrelated phenomenolgies, like multi-photon processes, non linear Compton scattering.