On the recurrence coefficients for the $q$-Laguerre weight and discrete Painlevé equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909431673913344 |
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| author | Hu, Jie Dzhamay, Anton Chen, Yang |
| author_facet | Hu, Jie Dzhamay, Anton Chen, Yang |
| contents | We study the dependence of recurrence coefficients in the three-term recurrence relation for orthogonal polynomials with a certain deformation of the $q$-Laguerre weight on the degree parameter $n$. We show that this dependence is described by a discrete Painlevé equation on the family of $A_{5}^{(1)}$ Sakai surfaces, but this equation is different from the standard examples of discrete Painlevé equations of this type and instead is a composition of two such. This case study is a good illustration of the effectiveness of a recently proposed geometric identification scheme for discrete Painlevé equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the recurrence coefficients for the $q$-Laguerre weight and discrete Painlevé equations Hu, Jie Dzhamay, Anton Chen, Yang Exactly Solvable and Integrable Systems Primary33C45, 34M55, 14E07, Secondary: 39A45, 33D45, 39A13 We study the dependence of recurrence coefficients in the three-term recurrence relation for orthogonal polynomials with a certain deformation of the $q$-Laguerre weight on the degree parameter $n$. We show that this dependence is described by a discrete Painlevé equation on the family of $A_{5}^{(1)}$ Sakai surfaces, but this equation is different from the standard examples of discrete Painlevé equations of this type and instead is a composition of two such. This case study is a good illustration of the effectiveness of a recently proposed geometric identification scheme for discrete Painlevé equations. |
| title | On the recurrence coefficients for the $q$-Laguerre weight and discrete Painlevé equations |
| topic | Exactly Solvable and Integrable Systems Primary33C45, 34M55, 14E07, Secondary: 39A45, 33D45, 39A13 |
| url | https://arxiv.org/abs/2412.13031 |