Buch, Englisch, 312 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 634 g
A Unified Theory Based on Singularities
Buch, Englisch, 312 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 634 g
ISBN: 978-0-19-850573-0
Verlag: OUP Oxford
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 valuable text and reference work.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
Weitere Infos & Material
- 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 Painlevé 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
