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Chapter 13 Confluent Hypergeometric Functions
A. B. Olde Daalhuis
School of Mathematics, Edinburgh University, Edinburgh, United Kingdom.
| Notation | 記法 | |
| 13.1 | Special Notation | 特殊表記 |
| Kummer Functions | Kummer関数 | |
| 13.2 | Definitions and Basic Properties | 定義と基本プロパティ |
| 13.3 | Recurrence Relations and Derivatives | 再発関係とデリバティブ |
| 13.4 | Integral Representations | 積分表現 |
| 13.5 | Continued Fractions | 連分数 |
| 13.6 | Relations to Other Functions | 他の機能との関係 |
| 13.7 | Asymptotic Expansions for Large Argument | Large 引数の漸近展開 |
| 13.8 | Asymptotic Approximations for Large Parameters | 大きなパラメーターの漸近近似 |
| 13.9 | Zeros | ゼロ |
| 13.10 | Integrals | 積分 |
| 13.11 | Series | 級数 |
| 13.12 | Products | プロダクツ |
| 13.13 | Addition and Multiplication Theorems | 足し算と乗算の定理 |
| Whittaker Functions | Whittaker 関数 | |
| 13.14 | Definitions and Basic Properties | 定義と基本プロパティ |
| 13.15 | Recurrence Relations and Derivatives | 再発関係とデリバティブ |
| 13.16 | Integral Representations | 積分表現 |
| 13.17 | Continued Fractions | 連分数 |
| 13.18 | Relations to Other Functions | 他の機能との関係 |
| 13.19 | Asymptotic Expansions for Large Argument | Large 引数の漸近展開 |
| 13.20 | Uniform Asymptotic Approximations for Large μ | Large の一様な漸近近似μ |
| 13.21 | Uniform Asymptotic Approximations for Large κ | Large の一様な漸近近似κ |
| 13.22 | Zeros | ゼロ |
| 13.23 | Integrals | 積分 |
| 13.24 | Series | 級数 |
| 13.25 | Products | プロダクツ |
| 13.26 | Addition and Multiplication Theorems | 足し算と乗算の定理 |
| Application | アプリケーション | |
| 13.27 | Mathematical Applications | 数学的応用 |
| 13.28 | Physical Applications | 物理的なアプリケーション |
| Computation | 計算 | |
| 13.29 | Methods of Computation | 計算方法 |
| 13.30 | Tables | テーブル |
| 13.31 | Approximations | 近似 |
| 13.32 | Software | ソフトウェア |