Chapter 31 Heun Functions
- Notes:
- The main references used in writing this chapter are Sleeman (1966a) and Ronveaux (1995). For additional bibliographic reading see Erdélyi et al. (1955).
- Referenced by:
- Brian D. Sleeman, Vadim B. Kuznetsov, Organization and Objective
- Permalink:
- http://dlmf.nist.gov/31
Department of Applied Mathematics,
University of Leeds,
Leeds, United Kingdom.
Department of Applied Mathematics,
University of Leeds,
Leeds, United Kingdom.
- Notation
-
Properties
- 31.2 Differential Equations
- 31.3 Basic Solutions
- 31.4 Solutions Analytic at Two Singularities: Heun Functions
- 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
- 31.6 Path-Multiplicative Solutions
- 31.7 Relations to Other Functions
- 31.8 Solutions via Quadratures
- 31.9 Orthogonality
- 31.10 Integral Equations and Representations
- 31.11 Expansions in Series of Hypergeometric Functions
- 31.12 Confluent Forms of Heun’s Equation
- 31.13 Asymptotic Approximations
- 31.14 General Fuchsian Equation
- 31.15 Stieltjes Polynomials
- Applications
- Computation