Heun's Differential Equations [Hardcover]

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 propagation, 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.

Preface
Introduction
A. Heun's Equation
1. General features of Heun's equation
2. Transformations of Heun's equation
3. Solutions of Heun's equation
I: General and power series
4. Solution of Heun's equation
II: Hypergeometric function series
5. Orthogonality relations
6. Integral equations and integral relations
Appendix
B. Confluent Heun Equation
1. General features of the confluent Heun equation
2. Solution of the confluent Heun equation
3. Confluent Heun functions
4. Asymptotic expansions
5. References
C. Double Confluent Heun Equation
1. General features of the DCHE
2. The analytic theory of the DCHE
3. Special results
4. References
D. Biconfluent Heun Equation
1. General features of BHE equation
2. Transformers of BHE equation
3. Solutions of the BHE equation
4. Integral relations
5. Miscellaneous
6. References
E. Triconfluent Heun Equation
1. General features of the THE equation
2. Transformations of the THE equation
3. Solutions of particular THE equations
4. Solutions in the vicinity of the singularity
5. Asymptotics with respect to a parameter
6. References
Addendum: Classification
1. Linear differential equations of second order with polynomial coefficients
2. The clal“0