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 Painlev� 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.

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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Special Functions : A Unified Theory Based on Singularities

Slavyanov, Sergei Yuryevitsh; Lay, Wolfgang

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