Special Functions A Unified Theory Based on Singularities [Hardcover]

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.

Preface
1. Linear Second-order ODE with Polynomial Coefficients
2. The Hypergeometric Class of Equations
3. The Heun Class of Equations
4. Application to Physical Sciences
5. The Painlev? Class of Equations
Appendix A: The Gamma Function and Related Functions
Appendix B: CTCPs for Heun Equations in General Form
Appendix C: Multipole Matrix Elements
Appendix D: SFTools - Database of the Special Functions
Bibliography
Index