Special Functions: A Unified Theory Based on Singularities

by Sergei Yu. Slavyanov, Wolfgang Lay

Overview

The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlevé equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a useful text and reference work.

Product Details

ISBN-13:	9780198505730
Publisher:	Oxford University Press
Publication date:	11/16/2000
Series:	Oxford Mathematical Monographs
Edition description:	New Edition
Pages:	312
Product dimensions:	5.90(w) x 9.00(h) x 0.90(d)

About the Author

St Petersburg State University

University of Stuttgart

Table of Contents

Preface1. Linear Second-order ODE with Polynomial Coefficients2. The Hypergeometric Class of Equations3. The Heun Class of Equations4. Application to Physical Sciences5. The Painlevé Class of EquationsAppendix A: The Gamma Function and Related FunctionsAppendix B: CTCPs for Heun Equations in General FormAppendix C: Multipole Matrix ElementsAppendix D: SFTools - Database of the Special FunctionsBibliographyIndex

Editorial Reviews

Slavyanov (St. Petersburg State U.) and Lay (U. Stuttgart) present a new theory of special functions as a field of knowledge lying at the intersection of mathematics, physics, and computer science. Chapters discuss linear second-order ODEs with polynomial coefficients; the hypergeometric class of equations; the Heun class of equations; application to physical sciences; and the Painlev<'e> class of equations. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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