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arXiv · 0905.2265

Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type

Nizar Demni
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Abstract

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.

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Nizar Demni. 2009-05-14. Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type. https://arxiv.org/abs/0905.2265

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