On spectral identities involving Gegenbauer polynomials

DOI10.1007/S41478-019-00163-7zbMath1428.33009OpenAlexW2911309330WikidataQ128491198 ScholiaQ128491198MaRDI QIDQ2335968

Richard Olu Awonusika

Publication date: 18 November 2019

Published in: The Journal of Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41478-019-00163-7

zbMATH Keywords

Gegenbauer polynomialsspecial functionsMaclaurin heat coefficientsGegenbauer coefficients

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (3)

On Jacobi polynomials \(\mathscr{P}_k^{(\alpha,\beta)}\) and coefficients \(c_j^{\ell}(\alpha,\beta)\) \((k\geq 0, \ell =5,6; 1\leq j\leq \ell; \alpha,\beta > -1)\) ⋮ On Jacobi polynomials and fractional spectral functions on compact symmetric spaces ⋮ Descriptions of fractional coefficients of Jacobi polynomial expansions

Cites Work

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• On Gegenbauer polynomials and coefficients \(c^{\ell}_{j}(\nu )(1\leq j\leq \ell, \nu >-1/2)\)
• Special function representations of the Poisson kernel on hyperbolic spaces
• Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere
• On Jacobi polynomials \((\mathcal {P}_k^{(\alpha, \beta)}: \alpha, \beta >-1)\) and Maclaurin spectral functions on rank one symmetric spaces
• A Spectral Identity on Jacobi Polynomials and its Analytic Implications
• Jacobi Polynomials, II. An Analytic Proof of the Product Formula

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