Special Functions: A Unified Theory Based on Singularities by Sergei Yuryevitsh Slavyanov

Special Functions: A Unified Theory Based on Singularities

bySergei Yuryevitsh Slavyanov, Wolfgang Lay

Hardcover | September 1, 2000

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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.

About The Author

Wolfgang Lay, Professor of Mathematics at the University of Stuttgart, Germany Sergei Yuryevitsh Slavyanov, Professor of Mathematics at the St. Petersburg State University, Russia

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Title:Special Functions: A Unified Theory Based on SingularitiesFormat: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