Notes on Umemura polynomials

DOI10.5802/afst.1658zbMath1470.33010OpenAlexW3154385875MaRDI QIDQ2664029

Masatoshi Noumi

Publication date: 20 April 2021

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/afst.1658

zbMATH Keywords

Umemura polynomial, Painlevé equation, Toda equation, special polynomial.

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (1)

A constructive proof for the Umemura polynomials of the third Painlevé equation

Cites Work

• Algebraic solutions of the sixth Painlevé equation
• Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Generalized Umemura polynomials.
• Special polynomials associated with the Painlevé equations. I
• BIRATIONAL WEYL GROUP ACTION ARISING FROM A NILPOTENT POISSON ALGEBRA
• Second proof of the irreducibility of the first differential equation of painlevé
• On a Class of Algebraic Solutions to the Painlevé VI Equation, Its Determinant Formula and Coalescence Cascade
• Middle convolution and deformation for Fuchsian systems
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