New kinds of deformed Bessel functions

Published 12 Jun 2012 in math.FA | (1206.2522v2)

Abstract: Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given with detailed proofs. Three more deformations are also outlined in the last section.

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