Awonusika, Richard Olu and Taheri, Ali (2017) On Gegenbauer polynomials and coefficients cℓj(ν) (1≤j≤ℓ, ν>−1/2). Results in Mathematics, 72 (3). pp. 1359-1367. 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:	27 Nov 2017 12:11
URI:	http://srodev.sussex.ac.uk/id/eprint/69243

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