Orthogonal Polynomials

• •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

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