Umemura polynomials for the Painlevé V equation

DOI10.1016/S0375-9601(98)00625-2zbMath0946.34077MaRDI QIDQ1966803

Masatoshi Noumi, Yasuhiko Yamada

Publication date: 8 March 2000

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

zbMATH Keywords

Schur functionsfifth Painlevé equationUmemura polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12)

Related Items (16)

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 ⋮ Geometric aspects of Painlevé equations ⋮ On the Umemura polynomials for the Painlevé III equation ⋮ 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 ⋮ 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 ⋮ 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 ⋮ A simplified version of higher covariant derivative regularization ⋮ The generalized Krawtchouk polynomials and the fifth Painlevé equation ⋮ Remarks on the Yablonskii-Vorob’ev polynomials

Cites Work

• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Rational solutions for the discrete Painlevé II equation.
• Determinant structure of the rational solutions for the Painlevé IV equation
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• Bilinear discrete Painleve-II and its particular solutions
• Determinant structure of the rational solutions for the Painlevé II equation

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