From Fourier to Gegenbauer: Dimension walks on spheres

2013/03/27 by Jochen Fiedler, Fiedler, Jochen
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Theory of Mathematics #Mathematical functions and polynomials #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1303.6856

openalex publication_date 2013/03/27 · arxiv created 2014/09/09 · arxiv updated 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the even- resp. odd-dimensional Schoenberg coefficients in Gegenbauer expansions of isotropic positive definite functions on the d-sphere can be expressed as linear combinations of Fourier resp. Legendre coefficients, and we give closed form expressions for the coefficients involved in these expansions.

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