Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI
Copyright policy )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. The non-linear difference equations form a pair of discrete Painlev�� equations and the differential equation is the $��$-form of the sixth Painlev�� equation. We briefly investigate the asymptotic behavior of the recurrence coefficients as $n\to \infty$ using the discrete Painlev�� equations.
- KU Leuven Belgium
- University of Warsaw Poland
Painlevé-type functions, 33C45, 42C05 (primary), 33C05, 34G20, 39A12 (secondary), discrete Painlevé equations, 0101 Pure Mathematics, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), 0102 Applied Mathematics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 4901 Applied mathematics, EQUATIONS, discrete Painleve equations, RECURRENCE COEFFICIENTS, Science & Technology, 0105 Mathematical Physics, Physics, discrete orthogonal polynomials, Physics, Mathematical, Painleve VI, Painlevé VI, Mathematics - Classical Analysis and ODEs, Physical Sciences, 4904 Pure mathematics, hypergeometric weights, Mathematics
Painlevé-type functions, 33C45, 42C05 (primary), 33C05, 34G20, 39A12 (secondary), discrete Painlevé equations, 0101 Pure Mathematics, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), 0102 Applied Mathematics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 4901 Applied mathematics, EQUATIONS, discrete Painleve equations, RECURRENCE COEFFICIENTS, Science & Technology, 0105 Mathematical Physics, Physics, discrete orthogonal polynomials, Physics, Mathematical, Painleve VI, Painlevé VI, Mathematics - Classical Analysis and ODEs, Physical Sciences, 4904 Pure mathematics, hypergeometric weights, Mathematics
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