Heun's Differential Equations
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Product details:
- Publisher OUP Oxford
- Date of Publication 19 October 1995
- ISBN 9780198596950
- Binding Hardback
- No. of pages380 pages
- Size 241x161x25 mm
- Weight 690 g
- Language English
- Illustrations 1 halftone, 3 tables 0
Categories
Short description:
Collating papers from a number of internationally renowned mathematicians, this book surveys both the current theory and the main areas of application of Heun's equation. This crops up in a wide variety of problems in applied mathematics, such as integral equations of potential theory, wave propagation, electrostatic oscillation, and Schrodinger's equation. This major collection will be of interest specifically for those researchers in non-linear Hamiltonian systems, as well as those working in mathematical biology.
MoreLong description:
Heun's equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger's equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).
There is a wealth of important results and open problems and the book is a welcome addition to the literature on these important special functions and their applications.
Table of Contents:
Preface
Introduction
A. Heun's Equation
General features of Heun's equation
Transformations of Heun's equation
Solutions of Heun's equation
I: General and power series
Solution of Heun's equation
II: Hypergeometric function series
Orthogonality relations
Integral equations and integral relations
Appendix
B. Confluent Heun Equation
General features of the confluent Heun equation
Solution of the confluent Heun equation
Confluent Heun functions
Asymptotic expansions
References
C. Double Confluent Heun Equation
General features of the DCHE
The analytic theory of the DCHE
Special results
References
D. Biconfluent Heun Equation
General features of BHE equation
Transformers of BHE equation
Solutions of the BHE equation
Integral relations
Miscellaneous
References
E. Triconfluent Heun Equation
General features of the THE equation
Transformations of the THE equation
Solutions of particular THE equations
Solutions in the vicinity of the singularity
Asymptotics with respect to a parameter
References
Addendum: Clssification
Linear differential equations of second order with polynomial coefficients
The classification scheme
Confluence Theorems
Tables
References
Bibliography
Author and Subject Index
