English

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}
}