On Gegenbauer polynomials and coefficients cℓj(ν) (1≤j≤ℓ, ν>−1/2)

Awonusika, Richard Olu and Taheri, Ali (2017) On Gegenbauer polynomials and coefficients cℓj(ν) (1≤j≤ℓ, ν>−1/2). Results in Mathematics. ISSN 1422-6383

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Abstract

The Gegenbauer coefficients cjℓ(ν)(1≤j≤ℓ, ν>−1/2) appear in the Maclaurin expansion of the heat kernels on the n-sphere and the real projective n-space. In this note we show that these coefficients can be computed by transforming the higher order derivative formula for the Gegenbauer polynomials Ckν(k≥0,ν>−1/2) into a spectral sum involving the powers of the eigenvalues of the associated Gegenbauer operator. We present explicit computations and various implications.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 13 Jul 2017 14:54
Last Modified: 18 Aug 2017 19:02
URI: http://sro.sussex.ac.uk/id/eprint/69243

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