Special functions: a unified theory based on singularities
Special functions: a unified theory based on singularities By Slavyanov S.Yu., Lay W.
2000 | 309 Pages | ISBN: 0198505736 | DJVU | 3 MB
2000 | 309 Pages | ISBN: 0198505736 | DJVU | 3 MB
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.