Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type
| dc.creator | Demni, Nizar | |
| dc.date | 2009-05-14 | |
| dc.date.accessioned | 2026-07-07T13:14:57Z | |
| dc.date.available | 2026-07-07T13:14:57Z | |
| dc.description | We work out the expression of the generalized Bessel function of type B in the two-rank case. This is done using Dijskma and Koornwinder's product formula for Jacobi polynomials and the obtained expression is given by multiple integrals involving only a normalized modified Bessel function and two symmetric Beta distributions. We think of that expression as the major step toward the explicit expression of the Dunkl's intertwining V operator reflections-invariant functions. Finally, we give in the same setting an explicit formula for the action of V on a product of a power of the norm and a spherical harmonic. The obtained formula extends to all dihedral systems and it improves the one derived by Y.Xu. | |
| dc.description | this paper is accepted for publication in Int. Trans. Spec. Funct | |
| dc.identifier | https://arxiv.org/abs/0905.2265 | |
| dc.identifier | http://arxiv.org/abs/0905.2265 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230344 | |
| dc.subject | Probability | |
| dc.title | Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type | |
| dc.type | text |