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Article Dans Une Revue Journal of Lie Theory Année : 2012

Generalized Bessel Function Associated with Dihedral Groups

Nizar Demni
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Résumé

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 D-n, n >= 2 when both multiplicities sum to an integer. In particular, we recover a previous result obtained for D-4 and we give a special interest to D-6. Finally, we derive similar results for odd dihedral groups.
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Dates et versions

hal-00688351 , version 1 (17-04-2012)

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  • HAL Id : hal-00688351 , version 1

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Nizar Demni. Generalized Bessel Function Associated with Dihedral Groups. Journal of Lie Theory, 2012, 22 (1), pp.81-91. ⟨hal-00688351⟩
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