Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI

We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second-order differential equation in one of the parameters of the weights. T...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2018
Hauptverfasser: Filipuk, G., Van Assche, W.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/209762
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Zitieren:Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Filipuk, G.
Van Assche, W.
author_facet Filipuk, G.
Van Assche, W.
citation_txt Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second-order differential equation in one of the parameters of the weights. The non-linear difference equations form a pair of discrete Painlevé equations, and the differential equation is the σ-form of the sixth Painlevé equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as n→∞ using the discrete Painlevé equations.
first_indexed 2025-12-03T12:22:44Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-209762
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-03T12:22:44Z
publishDate 2018
publisher Інститут математики НАН України
record_format dspace
spelling Filipuk, G.
Van Assche, W.
2025-11-26T11:23:17Z
2018
Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 33C45; 33E17; 34M55; 42C05
arXiv: 1804.02856
https://nasplib.isofts.kiev.ua/handle/123456789/209762
https://doi.org/10.3842/SIGMA.2018.088
We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second-order differential equation in one of the parameters of the weights. The non-linear difference equations form a pair of discrete Painlevé equations, and the differential equation is the σ-form of the sixth Painlevé equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as n→∞ using the discrete Painlevé equations.
GF acknowledges the support of the National Science Center (Poland) via grant OPUS 2017/25/B/BST1/00931. Support of the Alexander von Humboldt Foundation is also gratefully acknowledged. WVA is supported by FWO research project G.0864.16N and EOS project PRIMA 30889451. The authors thank the anonymous referees for their comments, which improved the original version.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
Article
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spellingShingle Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
Filipuk, G.
Van Assche, W.
title Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
title_full Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
title_fullStr Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
title_full_unstemmed Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
title_short Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
title_sort discrete orthogonal polynomials with hypergeometric weights and painlevé vi
url https://nasplib.isofts.kiev.ua/handle/123456789/209762
work_keys_str_mv AT filipukg discreteorthogonalpolynomialswithhypergeometricweightsandpainlevevi
AT vanasschew discreteorthogonalpolynomialswithhypergeometricweightsandpainlevevi