We consider a new class of Bessel functions, which are introduced by exploiting the property of quasi-monomiality of the Hermite polynomials. The use of Kampe de Feriet and of Bell type polynomials, allows extension of the definition of this class of functions, whose properties, including recurrences, differential equations they satisfy, addition and multiplication theorems, generating functions etc. are studied in detail. Possible applications of the Hermite-Bessel functions are also discussed.
All Science Journal Classification (ASJC) codes
Dattoli, G., Torre, A., & Carpanese, M. (1998). The hermite-bessel functions: A new point of view on the theory of the generalized bessel functions. Radiation Physics and Chemistry, 51(3), 221 - 228. https://doi.org/10.1016/S0969-806X(97)00261-2