Corpus ID: 15748538

New kinds of deformed Bessel functions

@article{Zahaf2012NewKO,
  title={New kinds of deformed Bessel functions},
  author={M. B. Zahaf and D. Manchon},
  journal={arXiv: Functional Analysis},
  year={2012}
}
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. 

References

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Singular polynomials for finite reflection groups
Dunkl operators for complex reflection groups
Integral kernels with reflection group invariance
A Treatise on the Theory of Bessel Functions
The wave equation for Dunkl operators
Deux resultats autour du theoreme de restriction de Chevalley
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