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A Generalized Freud Weight

Clarkson, Peter, Jordaan, Kerstin, Kelil, Abey (2015) A Generalized Freud Weight. Studies in Applied Mathematics, 136 (3). pp. 288-320. ISSN 0022-2526. E-ISSN 1467-9590. (doi:10.1111/sapm.12105)


We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a generalized Freud weight w(x;t)=|x|2?+1exp(?x4+tx2),x?R, with parameters ?>?1 and t?R, and classical solutions of the fourth Painlev\'e equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions that arise in the description of special function solutions of the fourth Painlev\'e equation. Further we derive a second-order linear ordinary differential equation and a differential-difference equation satisfied by the generalized Freud polynomials.

Item Type: Article
DOI/Identification number: 10.1111/sapm.12105
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Peter A Clarkson
Date Deposited: 20 Oct 2015 10:03 UTC
Last Modified: 29 May 2019 16:10 UTC
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