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mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property...

the n-body problem by Paul Painlevé Painlevé paradox, a paradox in rigid-body dynamics by Paul Painlevé Painlevé transcendents, ordinary differential equation...

{Ai}}(s),s\to \infty .} This function q {\displaystyle q} is a Painlevé transcendent. Other distributions are also expressible in terms of the same q...

functions, solving the remaining six equations, are called the Painlevé transcendents, and interest in them has revived recently due to their appearance...

B. (1980). "A boundary value problem associated with the second painlevé transcendent and the Korteweg-de Vries equation". Archive for Rational Mechanics...

differential equations, including work on Picard–Vessiot theory, Painlevé transcendents and his introduction of a kind of symmetry group for a linear differential...

for her research related to the theory of Mahler functions and Painlevé transcendents. In 1996 she published the first comprehensive text on transcendence...

exp(w). Lamé function Mathieu function Mittag-Leffler function Painlevé transcendents Parabolic cylinder function Arithmetic–geometric mean Ackermann...

Quantum Heisenberg model Hitchin system Mathematical physics Soliton Painleve transcendents Statistical mechanics Integrable algorithm Mark Ablowitz Rodney...

equations can be reduced to the famous sixth Painlevé equation. Motivated by the appearance of Painlevé transcendents in correlation functions in the theory...

other instances P I ⋯ P V {\displaystyle P_{I}\cdots P_{V}} of the Painlevé transcendents, for which numerous special solutions are also known. The fermionic...

Mittag-Leffler polynomials Mott polynomial Paul Painlevé: Painlevé function, Painlevé transcendents Poisson–Charlier polynomial Pollaczek polynomial...

thesis was entitled The Connection Problem for the First and Second Painlevé Transcendents. After a postdoctoral fellowship in 1987 and a research fellowship...

edition (2003) A S Fokas, A R Its, A A Kapaev and V Yu Novokshenov, Painlevé Transcendents: A Riemann-Hilbert Approach, AMS (2006) A S Fokas, A Unified Approach...

be described by an Integrable system. In a simple case, it is a Painlevé transcendent. The quantum correlation functions of a Tonks–Girardeau gas can...

the so-called Painlevé property: 'any movable singularity should be a pole', first used by Sofia Kovalevskaya. Painlevé transcendents Regular singular...

Louis Marie Henri Navier". MacTutor History of Mathematics archive. "Paul Painlevé". MacTutor History of Mathematics archive. "Louis Poinsot". MacTutor History...

integral operators to obtain explicit representations, in terms of Painlevé transcendents, of the limiting distributions of the largest and smallest eigenvalues...

theoretical physicists to use differential geometrical methods such as Painlevé transcendents and Lie theory for studying the integrability of chaotic systems...