Properties of Clifford-Legendre Polynomials

Title: Properties of Clifford-Legendre Polynomials
Creator: Ghaffari, Hamed Baghal; Hogan, Jeffrey A.; Lakey, Joseph D.
Relation: ARC.DP160101537 http://purl.org/au-research/grants/arc/DP160101537
Relation: Advances in Applied Clifford Algebras Vol. 32, Issue 1, no. 12
Publisher Link: http://dx.doi.org/10.1007/s00006-021-01179-8
Publisher: Birkhaeuser Science
Resource Type: journal article
Date: 2022
Description: Clifford-Legendre and Clifford–Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on m-dimensional euclidean space Rm and taking values in the associated Clifford algebra Rm. New recurrence and Bonnet-type formulae for these polynomials are provided, and their Fourier transforms are computed. Explicit representations in terms of spherical monogenics and Jacobi polynomials are given, with consequences including the interlacing of zeros. In the case m=2 we describe a degeneracy between the even- and odd-indexed polynomials.
Subject: Clifford-Legendre polynomials; bonnet formula; clifford analysis
Identifier: http://hdl.handle.net/1959.13/1483600
Identifier: uon:51143
Identifier: ISSN:0188-7009
Language: eng
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