Obtaining Generating Functions

Language: English

Published by Springer Berlin Heidelberg, 2012

3642876846 / 9783642876844

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783642876844

Title
Obtaining Generating Functions
Author
Elna B. McBride
Publisher
Springer Berlin Heidelberg
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642876846
ISBN 13
9783642876844
Item weight
184 grams
Dimensions
235x155x7 mm

AHA-BUCH GmbH

Einbeck, Germany

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