Special Functions: A Unified Theory Based on Singularities

Front Cover
Oxford University Press, 2000 - Mathematics - 293 pages
0 Reviews
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 will find this a useful text and reference work.

What people are saying - Write a review

We haven't found any reviews in the usual places.


Linear secondorder ODEs with polynomial coefficients
The hypergeometric class of equations
The Heun class of equations
Application to physical sciences
The Painleve class of equations
The gamma function and related functions
Multipole matrix elements
SFTools Database of the special functions

Common terms and phrases

References to this book

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

Bibliographic information