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Orthogonal Polynomials
Gabor Szegő

Colloquium Publications
1939; 432 pp; softcover
Volume: 23
Reprint/Revision History:
fourth edition 1975; tenth printing 1998; eleventh printing 2003 with corrections
ISBN-10: 0-8218-1023-5
ISBN-13: 978-0-8218-1023-1
List Price: US$54
Member Price: US$43.20
Order Code: COLL/23
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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

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
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