Relation of Semi-Classical Orthogonal Polynomials to General Schlesinger Systems via Twistor Theory

DOI10.1007/978-3-319-52842-7_12zbMath1404.34107OpenAlexW2631644614MaRDI QIDQ4645002

Hironobu Kimura

Publication date: 9 January 2019

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-52842-7_12

zbMATH Keywords

isomonodromic deformationtwistor theorysemi-classical orthogonal polynomial

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (1)

Matrix hypergeometric functions, semi-classical orthogonal polynomials and quantum Painlevé equations

Cites Work

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• The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
• Multivariate hypergeometric cascades, isomonodromy problems and Ward ansätze
• General Schlesinger Systems and Their Symmetry from the View Point of Twistor theory
• Painlevé VI and Hankel determinants for the generalized Jacobi weight
• Painlevé V and time-dependent Jacobi polynomials

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