数学常数 (以连分数表示排列)

這是以連分數表示排列的數學常數列表。
(無理數的常數有無限長的連分數：其最後面項為...。)
| 符號 | 數集 | 值 | 連分數表示 |
| --- | --- | --- | --- |
| Λ |   |  > – 2.7 · 10−9 |  |
| 0 |   \mathbb {N}  |  = 0  | [0;] |
| M1 |   |  ≈ 0.26149 72128 47642 78375 54268 38608 69585  | [0; 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1] |
| ½ |   \mathbb {Q}  |  = 0.5  | [0; 1, 1] |
| Ω 或 W(1) |   \mathbb {R}  |  ≈ 0.56714 32904 09783 87299 99686 62210 35555 | [0; 1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, 1, 1, 1, 1, 7, 1, 4, 2, ...] |
| γ |   |  ≈ 0.57721 56649 01532 86060 65120 90082 40243  | [0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 49, ...] |
|  \phi ^{-1} |   \mathbb {R} \backslash \mathbb {Q}  |  ≈ 0.61803 39887  | [0; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …] |
| C2 |   |  ≈ 0.66016 18158 46869 57392 78121 10014 55577  | [0; 1, 1, 1, 16, 2, 2, 2, 2, 1, 18, 2, 2, 11, 1, 1, 2, 4, 1, 16, 3, 2, 4, 21, 2, 405, 2, 1, 33, 1, 1] |
| β* |   |  ≈ 0.70258  | [0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5] |
| K |   \mathbb {R} \backslash \mathbb {Q} ?  |  ≈ 0.76422 36535 89220 66  | [0; 1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 7, 2, 3, 3, 18, 2, 1, 2, 1, 2, 1, 6] |
| B4 |   |  ≈ 0.87058 83800  | [0; 1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23] |
| K |   |  ≈ 0.91596 55941 77219 01505 46035 14932 38411  | [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2] |
| 1 |   \mathbb {N}  |  = 1  | [1;] |
| B´L |   |  ≈ 1.08366 （歷史上的猜測值，實際值為1） | [1; 11, 1, 20, 2, 1, 12, 2, 2] |
| K |   |  ≈ 1.13198 824  | [1; 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2] |
| ρ |   \mathbb {R}  |  ≈ 1.32471 95724 47460 25960 90885 44780 97340  | [1; 1, 3, 12, 1, 1, 3, 2, 3, 2, 4, 2, 141, 80, 2, 5, 1, 2, 8, 2, 1, 1, 3, 1, 8, 2, 1, 1, 14, 1, 1, 2, 1, 1, 1, 3, 1, 10, 4 ...] |
| √2 |   \mathbb {R} \backslash \mathbb {Q}  |  ≈ 1.41421 35623 73095 04880 16887 24209 69807  | [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,    2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...] |
| μ |  |  ≈ 1.45136 92348 83381 05028 39684 85892 027  | [1; 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, 4, 1, 12, 1, 1, 2, 2, 1, 7, 2, 1, 1, 1, 2, 30, 6, 3, 6] |
| EB |   \mathbb {R}  |  ≈ 1.60669 51524 15291 763  | [1; 1, 1, 1, 1, 5, 2, 1, 2, 29, 4, 1, 2, 2, 2, 2, 6, 1, 7, 1, 6, 2, 1, 1, 1, 20, 1, 3, 1, 1, 1, ...] |
| φ |   \mathbb {R} \backslash \mathbb {Q}  |  ≈ 1.61803 39887 49894 84820 45868 34365 63811  | [1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] |
| B2 |   |  ≈ 1.90216 05823  | [1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, 2, 2] |
| 2 |   \mathbb {N}  |  = 2  | [2;] |
| α |   |  ≈ 2.50290 78750 95892 82228 39028 73218 21578  | [2; 1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, 17, 1, 1, 5, 3, 2, 6, 3, 5, 1] |
| e |   \mathbb {R}  |  ≈ 2.71828 18284 59045 23536 02874 71352 66249  | [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1, ...] |
| K0 |   |  ≈ 2.68545 20011 19507 41674   | [2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90] |
| 3 |   \mathbb {N}  |  = 3  | [3;] |
| π |   \mathbb {R}  |  ≈ 3.14159 26535 89793 23846 26433 83279 50288  | [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, ...] |
| 4 |   \mathbb {N}  |  = 4  | [4;] |
| δ |   |  ≈ 4.66920 16091 02990 67185 32038 20466 20161  | [4; 1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, 1, 33, 1, 1, 53, 1, 1, 1, 1, 1] |