數學常數 (以連分數表示排列)

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]
```