Sergei Yu Slavyanov, Wolfgang Lay

Special Functions

A Unified Theory Based on Singularities

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Oxford University Press, USA
• Seitenzahl: 312
• Erscheinungstermin: 16. November 2000
• Englisch
• Abmessung: 234mm x 156mm x 19mm
• Gewicht: 612g
• ISBN-13: 9780198505730
• ISBN-10: 0198505736
• Artikelnr.: 24079801

Autorenporträt

Wolfgang Lay, Professor of Mathematics at the University of Stuttgart, Germany Sergei Yuryevitsh Slavyanov, Professor of Mathematics at the St. Petersburg State University, Russia

Inhaltsangabe

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