Special Functions: A Unified Theory Based on Singularities

Hardcover | September 1, 2000

bySergei Yuryevitsh Slavyanov, Wolfgang Lay

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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 ofthe 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 Painleve equations) are presented as a basic and new result. Manyapplications 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 valuable text andreference work.

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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 ofthe singularities serve as a basis for class...

Wolfgang Lay, Professor of Mathematics at the University of Stuttgart, Germany Sergei Yuryevitsh Slavyanov, Professor of Mathematics at the St. Petersburg State University, Russia
Format:HardcoverPublished:September 1, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198505736

ISBN - 13:9780198505730

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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 Painleve Class of EquationsA. Gamma-Function and Related FunctionsB. CTCPs for Heun Equations in General FormC. Multipole Matrix ElementsD. SFTools - Database of the Special Functions