Orthogonal Polynomials and Painleve Equations Van Assche Walter Katholieke Universiteit Leuven BelgiumPaperback

There are a number of intriguing connections between Painleve equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painleve transcendants and their use for local analysis near certain critical points helpful to their work. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painleve equations appear in mathematical analysis very useful.

Exercises throughout the book help the reader to get to grips with the material. Rational solutions and special function solutions of Painleve equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. The author is a leading authority on orthogonal polynomials, giving