Results of Heun Functions

Notation

31.1 Special 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

31.16 Mathematical Applications
31.17 Physical Applications

Computation

31.18 Methods of Computation