Special functions : a unified theory based on singularities
著者
書誌事項
Special functions : a unified theory based on singularities
（Oxford mathematical monographs）（Oxford science publications）
Oxford University Press, 2000
- : hbk
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注記
Includes bibliographical references (p. [286]-290) and index
内容説明・目次
内容説明
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 valuable text and reference work.
目次
- 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 Painleve Class of Equations
- A. Gamma-Function and Related Functions
- B. CTCPs for Heun Equations in General Form
- C. Multipole Matrix Elements
- D. SFTools - Database of the Special Functions
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