Classical transcendental solutions of the Painlevé equations and their degeneration

Abstract

We present a determinant expression for a family of classical transcendental solutions of the Painlevé V and the Painlevé VI equation. Degeneration of these solutions along the process of coalescence for the Painlevé equations is discussed.

arXiv comment22 pages

References in corpus (1)

• Higher order Painlevé equations of type $A_l^{(1)}$

Cited by in corpus (3)

• The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation
• Discrete Painlevé equations and random matrix averages
• Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations