数学常数 (以连分数表示排列)

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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 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]
1/2

\mathbb{Q}

= 0.5

[0; 1, 1]
ΩW(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;]
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]

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