Classical transcendental solutions of the Painlevé equations and their degeneration

DOI10.2748/tmj/1113246745zbMath1087.34063arXivnlin/0302026OpenAlexW2072591360MaRDI QIDQ1772204

Tetsu Masuda

Publication date: 15 April 2005

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0302026

zbMATH Keywords

Painlevé equationdegenerationclassical solutiondeterminant representation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

Special functions arising from discrete Painlevé equations: a survey ⋮ Explicit Formula and Extension of the Discrete Power Function Associated with the Circle Patterns of Schramm Type ⋮ Geometric aspects of Painlevé equations ⋮ The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation ⋮ Geometric description of a discrete power function associated with the sixth Painlevé equation ⋮ A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions ⋮ On Airy Solutions of the Second Painlevé Equation ⋮ Solutions of mixed Painlevé P_III—Vmodel ⋮ Hypergeometric solutions to Schrödinger equations for the quantum Painlevé equations ⋮ The generalized Krawtchouk polynomials and the fifth Painlevé equation

Cites Work

• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Affine Weyl groups, discrete dynamical systems and Painlevé equations
• Determinant structure of the rational solutions for the Painlevé IV equation
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• Confluence of cycles for hypergeometric functions on 𝑍_{2,𝑛+1}
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