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 

= 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 

= 0.5  [0; 1, 1] Ω 或 W(1) 

≈ 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, ...]   
≈ 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 
?  
≈ 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 

= 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 

≈ 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 

≈ 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 

≈ 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  
≈ 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 

= 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 

≈ 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 

= 3  [3;] π 

≈ 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 

= 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]

另見

 數學常數

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Category:連分數