Special Functions: A Unified Theory Based on Singularities

Presenting the topic of special functions in a different perspective, the authors have based the special functions on the theory of second-order ordinary differential equations in the complex domain. Several physical applications are presented, along with many tables and figures that help the readers find their way through the subject.
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 Painleve 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 should find this a useful text and reference work.