New kinds of deformed Bessel functions
Mohammed Brahim Zahaf (LPQ3M, LAPTH), Dominique Manchon
TL;DR
This paper introduces two novel deformations of Bessel functions using Dunkl calculus, exploring their properties and providing detailed proofs, while also outlining three additional deformations.
Contribution
The paper presents new deformed Bessel functions based on Dunkl calculus, expanding the mathematical framework and properties of these special functions.
Findings
Derived generating functions for the new deformed Bessel functions
Established differential-difference equations and recursive relations
Outlined three additional deformations of Bessel functions
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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Taxonomy
TopicsNonlinear Waves and Solitons · Mathematical functions and polynomials · Quantum Mechanics and Non-Hermitian Physics