Unique positive solution for an alternative discrete Painlevé I equation

Clarkson, Peter and Loureiro, Ana F. and Van Assche, Walter (2016) Unique positive solution for an alternative discrete Painlevé I equation. Journal of Difference Equations and Applications, . ISSN 1563-5120 (electronic) 1023-6198 (paper). (doi:https://doi.org/10.1080/10236198.2015.1127917) (Full text available)

Abstract

We show that the alternative discrete Painleve I equation has a unique solution which remains positive for all n >0. Furthermore, we identify this positive solution in terms of a special solution of the second Painleve equation involving the Airy function Ai(t). The special-function solutions of the second Painleve equation involving only the Airy function Ai(t) therefore have the property that they remain positive for all n>0 and all t>0, which is a new characterization of these special solutions of the second Painlevé equation and the alternative discrete Painlevé I equation.

Item Type: Article
Uncontrolled keywords: Discrete Painleve equation, Painlevé equation, Airy function, Orthogonal polynomials
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
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 10:08 UTC
Last Modified: 17 Jan 2017 11:10 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51098 (The current URI for this page, for reference purposes)
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