New kinds of deformed Bessel functions
  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. 
Mohammed Brahim Zahaf (LPQ3M, LAPTH), Dominique Manchon
math.FA