FUNK–HECKE FORMULA FOR ORTHOGONAL POLYNOMIALS ON SPHERES AND ON BALLS

YUAN XU

doi:10.1112/S0024609300007001

Abstract

Analogues of the Funk–Hecke formula for spherical harmonics are proved for Dunkl's h-harmonics associated to the reflection groups, and for orthogonal polynomials related to h-harmonics on the unit ball. In particular, an analogue and its application are discussed for the weight function (1−[mid ]x[mid ]2)μ−1/2 on the unit ball in ℝd.

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FUNK–HECKE FORMULA FOR ORTHOGONAL POLYNOMIALS ON SPHERES AND ON BALLS

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FUNK–HECKE FORMULA FOR ORTHOGONAL POLYNOMIALS ON SPHERES AND ON BALLS

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