Special Functions: A Unified Theory Based on Singularities

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Oxford University Press, 2000 - Mathematics - 293 pages
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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 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.
 

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Contents

Linear secondorder ODEs with polynomial coefficients
1
The hypergeometric class of equations
55
The Heun class of equations
97
Application to physical sciences
163
2
236
The gamma function and related functions
251
Multipole matrix elements
273
SF Tools Database of the special functions
281
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About the author (2000)

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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