Orthogonal Polynomials and Painlevé Equations

ISBN-13: 9781108441940 / Angielski / Miękka / 2017 / 190 str.

Walter Van Assche

Opis

A leading authority on orthogonal polynomials details their relationships with Painleve equations with clear proofs, examples, and exercises.

Spis treści

1. Introduction; 2. Freud weights and discrete Painlevé I; 3. Discrete Painlevé II; 4. Ladder operators; 5. Other semi-classical orthogonal polynomials; 6. Special solutions of Painlevé equations; 7. Asymptotic behavior of orthogonal polynomials near critical points; Appendix. Solutions to exercises; References; Index.