The third Painlev equation and associated special polynomials

DOI10.1088/0305-4470/36/36/306zbMath1046.33015OpenAlexW2135343206MaRDI QIDQ4468564

Peter A. Clarkson

Publication date: 10 June 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/36/36/306

zbMATH Keywords

Schur functionsdifferential-difference equationsToda equationsspecial polynomialsHamiltonian theory

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Difference equations (39A99) Painlevé-type functions (33E17) Hypergeometric functions (33C99)

Related Items (19)

Classical solutions of the degenerate fifth Painlevé equation ⋮ The fourth Painlevé equation and associated special polynomials ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ A computational exploration of the McCoy-Tracy-Wu solutions of the third Painlevé equation ⋮ A constructive proof for the Umemura polynomials of the third Painlevé equation ⋮ Painlevé analysis, Prelle–Singer approach, symmetries and integrability of damped Hénon–Heiles system ⋮ Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces ⋮ Differential equations for approximate solutions of Painlevé equations: application to the algebraic solutions of the Painlevé-III \((\mathrm{D}_7)\) equation ⋮ Single-user MIMO system, Painlevé transcendents, and double scaling ⋮ Similarity reductions of peakon equations: the $b$-family ⋮ A Fuchsian matrix differential equation for Selberg correlation integrals ⋮ The Yablonskii-Vorob'ev polynomials for the second Painlevé hierarchy ⋮ Discriminants of Umemura polynomials associated to Painlevé III ⋮ Special polynomials associated with rational solutions of the fifth Painlevé equation ⋮ Special polynomials associated with rational solutions of some hierarchies ⋮ Rational solutions of the Painlevé-III equation: large parameter asymptotics ⋮ On the algebraic solutions of the Painlevé-III (\(\mathrm{D}_7\)) equation ⋮ Wronskian Appell polynomials and symmetric functions ⋮ Similarity reductions of peakon equations: integrable cubic equations

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