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)
PDF
Author's Accepted Manuscript
Language: English |
|
Download this file (PDF/811kB) |
|
Request a format suitable for use with assistive technology e.g. a screenreader | |
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: | 01 Jul 2022 23:00 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/82162 (The current URI for this page, for reference purposes) |
- Link to SensusAccess
- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV
- Depositors only (login required):