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Obtaining Generating Functions

  • Elna Browning McBride

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 21)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Elna Browning McBride
    Pages 1-24
  3. Elna Browning McBride
    Pages 25-42
  4. Elna Browning McBride
    Pages 43-56
  5. Elna Browning McBride
    Pages 57-71
  6. Elna Browning McBride
    Pages 72-96
  7. Back Matter
    Pages 97-101

About this book

Introduction

This book is an introduction to the study of methods of obtaining generating functions. It is an expository work at the level of the beginning graduate student. The first part of Chapter I gives the reader the necessary definitions and basic concepts. The fundamental method of direct summation is explained and illustrated. The second part of Chapter I deals with the methods developed by Rainville. These methods are based principally on inventive manipulation of power series. Weisner's group-theoretic method is explained in detail in Chapter II and is further illustrated in Chapter III. When this method is applicable, it yields a set of at least three generating functions. In Chapter II for the Laguerre polynomials six generating functions were found. Truesdell's method is studied in Chapter IV. For a given set of functions {fez, an the success of this method depends on the existence of certain transformations. If fez, a) can be transformed into F(z, a) such that a a-; F(z, a)=F(z, a+ 1), or if fez, a) can be transformed into G(z, a) such that a a-; G(z, a)=G(z, a-I), then from each transformed function a generating function can be obtained. Truesdell's method for obtaining the transformed functions does not require any ingenuity on the user's part. Truesdell has shown how these simple results may be exploited to generate more complicated results by means of specified, systematic, and general processes. His method of obtaining generating functions is only one of these results.

Keywords

ETA Erzeugende Funktion Functions Rain concept eXist form formation function manipulation rating set transformation

Authors and affiliations

  • Elna Browning McBride
    • 1
  1. 1.Memphis State UniversityMemphisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-87682-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1971
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-87684-4
  • Online ISBN 978-3-642-87682-0
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site