This first detailed systematic treatment of orthogonal polynomials continues as a bestseller in the Colloquium Series

This is the first detailed systematic treatment of ... (a) the asymptotic behaviour of orthogonal polynomials, by various methods, with applications, in particular, to the `classical' polynomials of Legendre, Jacobi, Laguerre and Hermite; (b) a detailed study of expansions in series of orthogonal polynomials, regarding convergence and summability; (c) a detailed study of orthogonal polynomials in the complex domain; (d) a study of the zeros of orthogonal polynomials, particularly of the classical ones, based upon an extension of Sturm's theorem for differential equations. The book presents many new results; many results already known are presented in generalized or more precise form, with new simplified proofs.

-- Mathematical Reviews

*Preliminaries
*Definition of orthogonal polynomials; principal examples
*General properties of orthogonal polynomials
*Jacobi polynomials
*Laguerre and Hermite polynomials
*Zeros of orthogonal polynomials
*Inequalities
*Asymptotic properties of the classical polynomials
*Expansion problems associated with the classical polynomials
*Representation of positive functions
*Polynomials orthogonal on the unit circle
*Asymptotic properties of general orthogonal polynomials
*Expansion problems associated with general orthogonal polynomials
*Interpolation
*Mechanical quadrature
*Polynomials orthogonal on an arbitrary curve
*Problems and exercises
*Further problems and exercises
*Appendix
*List of references
*Further references
*Index