Orthogonal polynomials, Toda lattices and Painlevé equations

Abstract

We give a survey of the connection between orthogonal polynomials, Toda lattices and related lattices, and Painlevé equations (discrete and continuous).

References in corpus (5)

• Geometric Aspects of Painlevé Equations
• Painlevé V and time dependent Jacobi polynomials
• The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation
• Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations
• Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations

Cited by in corpus (2)

• On the recurrence coefficients for the $q$-Laguerre weight and discrete Painlevé equations
• Recurrence relations for the generalized Laguerre and Charlier orthogonal polynomials and discrete Painlevé equations on the $D_6^{(1)}$ Sakai surface