On the Umemura polynomials for the Painlevé III equation

DOI10.1016/S0375-9601(99)00577-0zbMath0939.34074arXivsolv-int/9903015OpenAlexW1991432053MaRDI QIDQ1966972

Tetsu Masuda, Kenji Kajiwara

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9903015

zbMATH Keywords

Laguerre polynomialsPainlevé III equations

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Ordinary differential equations on complex manifolds (34M45) Other special functions (33E99)

Related Items (24)

Classical solutions of the degenerate fifth Painlevé equation ⋮ FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS ⋮ On a q-Difference Painlevé III Equation: I. Derivation, Symmetry and Riccati Type Solutions ⋮ Generating functions related to the Okamoto polynomials for the Painlevé IV equation ⋮ The fourth Painlevé equation and associated special polynomials ⋮ Special polynomials associated with the fourth order analogue to the Painlevé equations ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ A constructive proof for the Umemura polynomials of the third Painlevé equation ⋮ Single-user MIMO system, Painlevé transcendents, and double scaling ⋮ Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions ⋮ Geometric aspects of Painlevé equations ⋮ Stationary axisymmetric solutions involving a third order equation irreducible to Painlevé transcendents ⋮ The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials ⋮ 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 ⋮ A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions ⋮ On Gorenstein surfaces dominated by P² ⋮ On a q-Difference Painlevé III Equation: II. Rational Solutions ⋮ On Vortex Solutions and Links between the Weierstrass System and the Complex Sine-Gordon Equations ⋮ Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian ⋮ Wronskian Appell polynomials and symmetric functions ⋮ A simplified version of higher covariant derivative regularization ⋮ Universal characters, integrable chains and the Painlevé equations

Cites Work

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• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Umemura polynomials for the Painlevé V equation
• Coalescence cascades and special-function solutions for the continuous and discrete Painlevé equations
• Determinant structure of the rational solutions for the Painlevé IV equation
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• Bäcklund Transformations and Solution Hierarchies for the Third Painlevé Equation
• A study of the alternate discrete Painlevé II equation
• Classical solutions of the third Painlevé equation
• Determinant structure of the rational solutions for the Painlevé II equation
• Rational Solutions of Painlevé Equations

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