rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Asymptotics for orthogonal polynomials
  name:
    name part: Assche, Walter van
    name part: 1958-
    role:
      role term: creator
  name:
    name part: Assche, Walter van
    name part: 1958-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1987
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (vi, 201 pages) : illustrations.
  abstract: Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrdinger operators, illustrating the close interaction with different branches of applied mathematics.
  table of contents: Introduction -- Orthogonal Polynomials on a Compact Set -- Asymptotically Periodic Recurrence Coefficients -- Probabilistic Proofs of Asymptotic Formulas -- Orthogonal Polynomials on Unbounded Sets -- Zero Distribution and Consequences -- Some Applications -- Appendix -- References -- Subject Index.
  note: Walter van Assche.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (pages 181-195) and index.
  subject:
    topic: Orthogonal polynomials
    topic: Asymptotic theory
  subject:
    topic: transformation Stieltjes
  subject:
    topic: probabilités
  subject:
    topic: périodicité
  subject:
    topic: théorie asymptotique
  subject:
    topic: polynômes orthogonaux
  subject:
    topic: Polynômes orthogonaux
    topic: Théorie asymptotique
  subject:
    topic: Orthogonal polynomials
    topic: Asymptotic theory
  subject:
    topic: Polynômes orthogonaux
    topic: Théorie asymptotique
  subject:
    topic: Orthogonale Polynome
  subject:
    topic: Asymptotik
  classification: QA3 .L28 no. 1265
  classification: QA404.5
  classification: 515.55
  classification: 31.35
  related item:
    title info:
      title: Asymptotics for orthogonal polynomials
    name:
      name part: Assche, Walter van, 1958-
    origin info:
      publisher: Berlin ; New York : Springer-Verlag, ©1987
    identifier: (DLC) 87015495
    identifier: (OCoLC)16131911
  related item:
    title info:
      title: Lecture notes in mathematics (Springer-Verlag) ; 1265
  identifier: 9783540477112 (electronic bk.)
  identifier: 354047711X (electronic bk.)
  identifier: 0387180230
  identifier: 9780387180236
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: SPLNM
    record creation date: 081208
    record change date: 20260422180254.6
    record identifier: in00003500411
    language of cataloging:
      language term: eng