Properties of Clifford Legendre Polynomials

2020/12/10 by Ghaffari, Hamed Baghal, Hogan, Jeffrey A., Lakey, Joseph D. · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.05469

Abstract

Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on m-dimensional euclidean space \mathbb R^m and taking values in the associated Clifford algebra \mathbb R_m. New recurrence and Bonnet type formulae for these polynomials are proved, as their Fourier transforms are computed. Explicit representations in terms of spherical monogenics and Jacobi polynomials are given, with consequences including the interlacing of the zeros. In the case m=2 we describe a degeneracy between the even- and odd-indexed polynomials.

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