Abstract
Generalized Bessel functions (GBF) have proved a powerful tool to investigate the dynamical aspects of physical problems such as electron scattering by an intense linearly polarized laser wave, multiphoton processes and undulator radiation. The analytical and numerical study of GBF's has revealed their interesting properties, which in some sense can be regarded as an extension of the properties of the ordinary Bessel functions (BF) to a two-dimensional domain. In this connection, the relevance of GBF's and their multivariable extension in mathematical physics has been emphasized, since they provide analytical solutions to partial differential equations such as the multidimensional diffusion equation, the Schrödinger and Klein-Gordon equations. The algebraic structure underlying GBF's can be recognized in full analogy with BF's, thus providing a unifying view to the theory of both BF's and GBF's.
Published Version
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