Colloquium Publications 1939; 432 pp; softcover Volume: 23 Reprint/Revision History: fourth edition 1975; tenth printing 1998; eleventh printing 2003 with corrections ISBN10: 0821810235 ISBN13: 9780821810231 List Price: US$54 Member Price: US$43.20 Order Code: COLL/23
 This first detailed systematic treatment of orthogonal polynomials continues as a bestseller in the Colloquium Series. Reviews "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 Table of Contents  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
