Chapter 16 Generalized Hypergeometric Functions and Meijer
G-Function
R. A. Askey
Department of Mathematics, University of Wisconsin, Madison, Wisconsin.
A. B. Olde Daalhuis
School of Mathematics, Edinburgh University, Edinburgh, United Kingdom.
| Notation | 記法 | |
| 16.1 | Special Notation | 特殊表記 |
| Generalized Hypergeometric Functions | 一般化超幾何関数 | |
| 16.2 | Definition and Analytic Properties | 定義および解析プロパティ |
| 16.3 | Derivatives and Contiguous Functions | 導関数と隣接関数 |
| 16.4 | Argument Unity | 引数の統一性 |
| 16.5 | Integral Representations and Integrals | 積分表現と積分 |
| 16.6 | Transformations of Variable | 変数の変換 |
| 16.7 | Relations to Other Functions | 他の機能との関係 |
| 16.8 | Differential Equations | 微分方程式 |
| 16.9 | Zeros | ゼロ |
| 16.10 | Expansions in Series of pFq Functions | シリーズの拡張Fqp関数 |
| 16.11 | Asymptotic Expansions | 漸近展開 |
| 16.12 | Products | プロダクツ |
| Two-Variable Hypergeometric Functions | 2 変数超幾何関数 | |
| 16.13 | Appell Functions | Appell 関数 |
| 16.14 | Partial Differential Equations | 偏微分方程式 |
| 16.15 | Integral Representations and Integrals | 積分表現と積分 |
| 16.16 | Transformations of Variables | 変数の変換 |
| Meijer G-Function | メイジャーG-関数 | |
| 16.17 | Definition | 定義 |
| 16.18 | Special Cases | 特殊なケース |
| 16.19 | Identities | アイデンティティ |
| 16.20 | Integrals and Series | 積分と級数 |
| 16.21 | Differential Equation | 微分方程式 |
| 16.22 | Asymptotic Expansions | 漸近展開 |
| Applications | アプリケーション | |
| 16.23 | Mathematical Applications | 数学的応用 |
| 16.24 | Physical Applications | 物理的なアプリケーション |
| Computation | 計算 | |
| 16.25 | Methods of Computation | 計算方法 |
| 16.26 | Approximations | 近似 |
| 16.27 | Software | ソフトウェア |