Generalized Bessel Function Associated with Dihedral Groups
Journal of Lie Theory, Tome 22 (2012) no. 1, pp. 81-91
Voir la notice de l'article provenant de la source Heldermann Verlag
Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas for Fourier and Radon transforms to derive a closed formula for this series when the parameter of the Gegenbauer polynomial is a positive integer. As a by-product, we get a relatively simple integral representation for the generalized Bessel function associated with dihedral groups Dn, n ≥ 2 when both multiplicities sum to an integer. In particular, we recover a previous result obtained for D4 and we give a special interest to D6. Finally, we derive similar results for odd dihedral groups.
Classification :
33C52, 33C45, 42C10, 43A85, 43A90
Mots-clés : Generalized Bessel function, dihedral groups, Jacobi polynomials, Radon Transform
Mots-clés : Generalized Bessel function, dihedral groups, Jacobi polynomials, Radon Transform
Affiliations des auteurs :
Nizar Demni 1
Nizar Demni. Generalized Bessel Function Associated with Dihedral Groups. Journal of Lie Theory, Tome 22 (2012) no. 1, pp. 81-91. http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a2/
@article{JOLT_2012_22_1_a2,
author = {Nizar Demni},
title = {Generalized {Bessel} {Function} {Associated} with {Dihedral} {Groups}},
journal = {Journal of Lie Theory},
pages = {81--91},
year = {2012},
volume = {22},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_1_a2/}
}