Skip to main content

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) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:82162)

PDF Author's Accepted Manuscript
Language: English

Restricted to Repository staff only until 1 July 2022.
Contact us about this Publication
[thumbnail of SexticFreudWeight_R2.pdf]
Official URL
https://doi.org/10.1080/10652469.2020.1798949

Abstract

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: 21 Sep 2021 14:27 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/82162 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
  • Depositors only (login required):