From Fourier to Gegenbauer: Dimension walks on spheres
Statistics Theory
2014-09-10 v2 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1303.6856,
title = {From Fourier to Gegenbauer: Dimension walks on spheres},
author = {Jochen Fiedler},
journal= {arXiv preprint arXiv:1303.6856},
year = {2014}
}