© 1987

Asymptotics for Orthogonal Polynomials

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1265)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Walter Van Assche
    Pages 1-13
  3. Walter Van Assche
    Pages 14-42
  4. Walter Van Assche
    Pages 43-86
  5. Walter Van Assche
    Pages 87-104
  6. Walter Van Assche
    Pages 105-137
  7. Walter Van Assche
    Pages 138-163
  8. Walter Van Assche
    Pages 164-174
  9. Back Matter
    Pages 175-201

About this book


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 Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.


applied mathematics complex analysis distribution measure orthogonal polynomials scattering theory schrödinger operator

Bibliographic information

  • Book Title Asymptotics for Orthogonal Polynomials
  • Authors Walter Van Assche
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-18023-4
  • eBook ISBN 978-3-540-47711-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VI, 206
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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