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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mathematical constants by continued fraction representation ： ウィキペディア英語版 Mathematical constants by continued fraction representation This is a list of mathematical constants sorted by their representations as continued fractions. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are known. || $\backslash mathbb\backslash setminus\backslash mathbb$ || 0.61803 39887 || (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, … ) || irrational |- | $C$ || $\backslash mathbb$ || 0.64341 05463 || (1, 1, 1, 22, 32, 132, 1292, 252982, 4209841472, 2694251407415154862, … ) || All terms are squares and truncated at 10 terms due to large size. |- | $C\_2$ || $\backslash mathbb$ || 0.66016 18158 || (1, 1, 1, 16, 2, 2, 2, 2, 1, 18, 2, 2, 11, 1, 1, 2, 4, 1, 16, 3, … ) || Hardy–Littlewood's twin prime constant. Presumed irrational, but not proved. |- | $\backslash gamma$ || $\backslash mathbb$ || 0.57721 56649 || (1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, … ) || Presumed irrational, but not proved. |- | $\backslash Omega$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 0.56714 32904 || (1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, … ) || |- | $\backslash beta^\backslash star$ || $\backslash mathbb$ || 0.70258 || (1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5, … ) || Value only known to 5 decimal places. |- | $K$ || $\backslash mathbb\; (\backslash setminus\backslash mathbb?)$ || 0.76422 36535 || (1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 7, 2, … ) || May have been proven irrational. |- | $\backslash frac\; 1$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 0.83462 68417 || (1, 5, 21, 3, 4, 14, 1, 1, 1, 1, 1, 3, 1, 15, 1, 3, 8, 36, 1, 2, … ) || Gauss's constant |- | $B\_4$ || $\backslash mathbb$ || 0.87058 83800 || (1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23, … ) || Brun's prime quadruplet constant. Estimated value; 99% confidence interval ± 0.00000 00005. |- | $C\_2$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 0.86224 01259 || (1, 6, 3, 1, 6, 5, 3, 3, 1, 6, 4, 1, 3, 298, 1, 6, 1, 1, 3, 285, … ) || Base 2 Champernowne constant. The binary expansion is $C\_2\; =\; 0.1\; 10\; 11\; 100\; 101\; 110\; 111\; 1000\backslash ldots\_2$ |- | $G$ || $\backslash mathbb$ || 0.91596 55942 || (1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, … ) || Presumed irrational, but not proved. |- | $\backslash frac\; 12$ || $\backslash mathbb$ || 0.50000 00000 || (2 ) || |- | $\backslash beta$ || $\backslash mathbb$ || 0.28016 94990 || (3, 1, 1, 3, 9, 6, 3, 1, 3, 13, 1, 16, 3, 3, 4, … ) || Presumed irrational, but not proved. |- | $M$ || $\backslash mathbb$ || 0.26149 72128 || (3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, … ) || Presumed irrational, but not proved. |- | $C\_$ || $\backslash mathbb$ || 0.18785 96424 || (5, 3, 10, 1, 1, 4, 1, 1, 1, 1, 9, 1, 1, 12, 2, 17, 2, 2, 1, 1, … ) || |- | $C\_$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 0.12345 67891 || (8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, $4.57540\backslash times\; 10^$, 6, 1, … ) || Base 10 Champernowne constant. Champernowne constants in any base exhibit sporadic large numbers; the 40th term in $C\_$ has 2504 digits. |- | $1$ || $\backslash mathbb$ || 1.00000 00000 || () || |- | $\backslash phi$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 1.61803 39887 || (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, … ) || |- | $E$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 1.60669 51524 || (1, 1, 1, 1, 5, 2, 1, 2, 29, 4, 1, 2, 2, 2, 2, 6, 1, 7, 1, 6, … ) || Not known whether algebraic or transcendental. |- | $B\_2$ || $\backslash mathbb$ || 1.90216 05823 || (1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, … ) || Brun's twin prime constant. Estimated value; best bounds |- | $\backslash sqrt\; 2$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 1.41421 35624 || (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, … ) || |- | $\backslash mu$ || $\backslash mathbb$ || 1.45136 92349 || (2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, 4, 1, 12, 1, 1, 2, 2, 1, … ) || Presumed irrational, but not proved. |- | $B$ || $\backslash mathbb$ || 1.45607 49485 || (2, 5, 5, 4, 1, 1, 18, 1, 1, 1, 1, 1, 2, 13, 3, 1, 2, 4, 16, 4, … ) || |- | $\backslash rho$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 1.32471 95724 || (3, 12, 1, 1, 3, 2, 3, 2, 4, 2, 141, 80, 2, 5, 1, 2, 8, 2, 1, 1, … ) || |- | $\backslash zeta(3)$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 1.20205 69032 || (4, 1, 18, 1, 1, 1, 4, 1, 9, 9, 2, 1, 1, 1, 2, 7, 1, 1, 7, 11, … ) || |- | $V$ || $\backslash mathbb$ || 1.13198 82488 || (7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2, … ) || Viswanath's constant. Apparently, Eric Weisstein calculated this constant to be approximately 1.13215 06911 with Mathematica. |- | $2$ || $\backslash mathbb\; N$ || 2.00000 00000 || () || |- | $2^\backslash sqrt\; 2$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 2.66514 41426 || (1, 1, 1, 72, 3, 4, 1, 3, 2, 1, 1, 1, 14, 1, 2, 1, 1, 3, 1, 3, … ) || |- | $\backslash alpha$ || $\backslash mathbb$ || 2.50290 78751 || (1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, … ) || |- | $e$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 2.71828 18285 || (1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, … ) || |- | $K\_0$ || $\backslash mathbb$ || 2.68545 20011 || (1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, … ) || |- | $F$ || $\backslash mathbb$ || 2.80777 02420 || (1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, 1, 1, 1, 5, 1, 1, 1, … ) || |- | $P\_2$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 2.29558 71494 || (3, 2, 1, 1, 1, 1, 3, 3, 1, 1, 4, 2, 3, 2, 7, 1, 6, 1, 8, 7, … ) || |- | $3$ || $\backslash mathbb$ || 3.00000 00000 || () || |- | $\backslash psi$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 3.35988 56662 || (2, 1, 3, 1, 1, 13, 2, 3, 3, 2, 1, 1, 6, 3, 2, 4, 362, 2, 4, 8, … ) || |- | $\backslash pi$ || $\backslash mathbb\backslash setminus\backslash mathbb$ || 3.14159 26536 || (7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, … ) || |- | $4$ || $\backslash mathbb\; N$ || 4.00000 00000 || () || |- | $\backslash delta$ || $\backslash mathbb\; R$ || 4.66920 16091 || (1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, … ) || |- | $5$ || $\backslash mathbb\; N$ || 5.00000 00000 || () || |- | $e^\backslash pi$ || $\backslash mathbb\; R\backslash setminus\backslash mathbb\; A$ || 23.14069 26328 || (7, 9, 3, 1, 1, 591, 2, 9, 1, 2, 34, 1, 16, 1, 30, 1, 1, 4, 1, 2, … ) || Gelfond's constant. Can also be expressed as $(-1)^$; from this form, it is transcendental due to the Gelfond–Schneider theorem. |} ==See also== * Physical constant * Mathematical constants and functions 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mathematical constants by continued fraction representation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.