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A generalized sextic Freud weight

Clarkson, Peter, Jordaan, Kerstin (2021) A generalized sextic Freud weight. Integral Transforms and Special Functions, 32 (5-8). pp. 458-482. ISSN 1065-2469. (doi:10.1080/10652469.2020.1798949) (KAR id:82162)


We discuss the recurrence coefficients of orthogonal polynomials with respect to a generalised sextic Freud weight ω(x;t, λ) = |x|\(^{2λ+1}\), x ∈ R, with parameters λ > −1 and t ∈ R. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of generalised hypergeometric functions 1F2(a1; b1, b2; z). We derive a nonlinear discrete as well as a system of differential equations satisfied by the recurrence coefficients and use these to investigate their asymptotic behaviour. We conclude by highlighting a fascinating connection between generalised quartic, sextic, octic and decic Freud weights when expressing their first moments in terms of generalised hypergeometric functions.

Item Type: Article
DOI/Identification number: 10.1080/10652469.2020.1798949
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Clarkson
Date Deposited: 20 Jul 2020 12:12 UTC
Last Modified: 01 Jul 2022 23:00 UTC
Resource URI: (The current URI for this page, for reference purposes)

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