Double Gegenbauer expansion of |s–t|α

DOI10.1080/10652469.2019.1585433zbMath1412.42066arXiv1902.08064OpenAlexW3104744917MaRDI QIDQ5742556

Toshiyuki Kobayashi, Alex Leontiev

Publication date: 15 May 2019

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08064

zbMATH Keywords

Hermite polynomialSobolev inequalityGegenbauer polynomialSelberg integral

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Semisimple Lie groups and their representations (22E46) Differential geometry of symmetric spaces (53C35) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

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• Generalized Bernstein-Reznikov integrals
• The \({\mathfrak{sl}}_3\) Selberg integral
• Selberg-type integrals associated with \(\mathfrak{sl}_3\)
• On a generalization of the generating function for Gegenbauer polynomials
• Symmetry breaking for representations of rank one orthogonal groups
• The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞)
• Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (−1, 1)
• The importance of the Selberg integral

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