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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209762 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862541903009939456 |
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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.
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| first_indexed | 2025-12-03T12:22:44Z |
| format | Article |
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| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI Article published earlier |
| 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 |