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Chapter 31 Heun Functions
B. D. Sleeman
Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom.
V. B. Kuznetsov
Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom.
| Notation | 記法 | |
| 31.1 | Special Notation | 特殊表記 |
| Properties | プロパティ | |
| 31.2 | Differential Equations | 微分方程式 |
| 31.3 | Basic Solutions | 基本的なソリューション |
| 31.4 | Solutions Analytic at Two Singularities: Heun Functions | 2つの特異点における解解析:Heun関数 |
| 31.5 | Solutions Analytic at Three Singularities: Heun Polynomials | 3つの特異点における解解析:Heun多項式 |
| 31.6 | Path-Multiplicative Solutions | パス乗算解 |
| 31.7 | Relations to Other Functions | 他の機能との関係 |
| 31.8 | Solutions via Quadratures | 直交による解法 |
| 31.9 | Orthogonality | 直交 |
| 31.10 | Integral Equations and Representations | 積分方程式と表現 |
| 31.11 | Expansions in Series of Hypergeometric Functions | 一連の超幾何関数の展開 |
| 31.12 | Confluent Forms of Heun’s Equation | Heunの方程式の合流形式 |
| 31.13 | Asymptotic Approximations | 漸近近似 |
| 31.14 | General Fuchsian Equation | 一般フクシアン方程式 |
| 31.15 | Stieltjes Polynomials | Stieltjes多項式 |
| Applications | アプリケーション | |
| 31.16 | Mathematical Applications | 数学的応用 |
| 31.17 | Physical Applications | 物理的なアプリケーション |
| Computation | 計算 | |
| 31.18 | Methods of Computation | 計算方法 |