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Polynomial Expansions of Analytic Functions

  • Authors
  • Ralph P. BoasJr.
  • R. Creighton Buck
Book

Part of the Ergebnisse der Mathematik und Ihrer Grenzgebiete book series (MATHE2, volume 19)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Ralph P. Boas Jr., R. Creighton Buck
    Pages 1-21
  3. Ralph P. Boas Jr., R. Creighton Buck
    Pages 21-47
  4. Ralph P. Boas Jr., R. Creighton Buck
    Pages 47-66
  5. Ralph P. Boas Jr., R. Creighton Buck
    Pages 66-71
  6. Back Matter
    Pages 71-77

About this book

Introduction

This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop­ erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH'S mono­ graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa­ tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.

Keywords

Analytic Functions Complex analysis Funktionentheorie analytic function function mathematics

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-87887-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1958
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-87889-3
  • Online ISBN 978-3-642-87887-9
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site
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