Classical transcendental solutions of the Painlevé equations and their degeneration
Copyright policy )Classical transcendental solutions of the Painlevé equations and their degeneration
We present a determinant expression for a family of classical transcendental solutions of the Painlev�� V and the Painlev�� VI equation. Degeneration of these solutions along the process of coalescence for the Painlev�� equations is discussed.
22 pages
- Kobe University Japan
Nonlinear Sciences - Exactly Solvable and Integrable Systems, degeneration, FOS: Physical sciences, 33C05, 33C15, determinant representation, Painlevé equation, classical solution, Classical hypergeometric functions, \({}_2F_1\), 34M55, 33E17, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Exactly Solvable and Integrable Systems (nlin.SI)
Nonlinear Sciences - Exactly Solvable and Integrable Systems, degeneration, FOS: Physical sciences, 33C05, 33C15, determinant representation, Painlevé equation, classical solution, Classical hypergeometric functions, \({}_2F_1\), 34M55, 33E17, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Exactly Solvable and Integrable Systems (nlin.SI)
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