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Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\sigma$-form of the sixth Painlevé equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as $n\to \infty$ using the discrete Painlevé equations.
Keywords: discrete orthogonal polynomials; hypergeometric weights; discrete Painlevé equations; Painlevé VI. 
@article{SIGMA_2018_14_a87,
     author = {Galina Filipuk and Walter Van Assche},
     title = {Discrete {Orthogonal} {Polynomials} with {Hypergeometric} {Weights} and {Painlev\'e} {VI}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2018},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a87/}
}
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Galina Filipuk; Walter Van Assche. Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a87/

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