On the Umemura Polynomials for the Painlevé III equation
arXiv:solv-int/9903015 · doi:10.1016/S0375-9601(99)00577-0
Abstract
A determinant expression for the rational solutions of the Painlevé III (P) equation whose entries are the Laguerre polynomials is given. Degeneration of this determinant expression to that for the rational solutions of P is discussed by applying the coalescence procedure.
10 pages, LaTeX 2.09(Elsevier style), submitted to Phys. Lett. A
References in corpus (2)
Cited by in corpus (19)
- Geometric Aspects of Painlevé Equations
- On a q-difference Painlevé III equation: I. Derivation, symmetry and Riccati type solutions
- The Yablonskii - Vorob'ev polynomials for the second Painlev'e hierarchy
- A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions
- On a q-difference Painlevé III equation: II. Rational solutions
- Classical Solutions of the Degenerate Fifth Painlevé Equation
- Special polynomials associated with the fourth order analogue to the Painlev'e equations
- Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
- Wronskian Appell Polynomials and Symmetric Functions
- On a class of algebraic solutions to Painlevé VI equation, its determinant formula and coalescence cascade
- Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation
- A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation
- Explicit form of the Yablonskii - Vorob'ev polynomials
- Multivortex Solutions of the Weierstrass Representation
- Polynomial Solutions to Difference Equations Connected to Painleve' II-VI
- A Determinant Formula for a Class of Rational Solutions of Painlevé V Equation
- Lectures on exceptional orthogonal polynomials and rational solutions to Painlevé equations
- Painlevé-III Monodromy Maps Under the Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions
- Single-use MIMO system, Painlevé transcendents and double scaling