Dzhamay, A;
Filipuk, G;
Stokes, A;
(2021)
On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials.
Integral Transforms and Special Functions
, 32
(5-8)
pp. 483-492.
10.1080/10652469.2020.1809391.
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Abstract
In this paper we present a connection between systems of differential equations for the recurrence coefficients of polynomials orthogonal with respect to the generalized Meixner and the deformed Laguerre weights. It is well-known that the recurrence coefficients of both generalized Meixner and deformed Laguerre orthogonal polynomials can be expressed in terms of solutions of the fifth Painlevé equation but no explicit relation between systems of differential equations for the recurrence coefficients was known. We also present certain limits in which the recurrence coefficients can be expressed in terms of solutions of the Painlevé XXXIV equation, which in the deformed Laguerre case extends previous studies and in the generalized Meixner case is a new result.
| Type: | Article |
|---|---|
| Title: | On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/10652469.2020.1809391 |
| Publisher version: | https://doi.org/10.1080/10652469.2020.1809391 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Orthogonal polynomials, Painlevé equations |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10132074 |
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