# Obtaining Generating Functions

• Elna Browning McBride
Book

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

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

### 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
• Print ISBN 978-3-642-87684-4
• Online ISBN 978-3-642-87682-0
• Series Print ISSN 0081-3877
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