수학 상수 목록

수학 상수는 값이 여러 수학 문제에서 쉽게 사용할 수 있도록 하기 위해 종종 기호(예: 알파벳 문자) 또는 수학자 이름으로 언급되는 모호하지 않은 정의에 의해 고정되는 핵심 숫자입니다.^[1]예를 들어, 일정한 π은 원의 둘레 길이와 지름의 비율로 정의될 수 있습니다.다음 목록에는 발견 연도별로 순서를 매긴 각 숫자를 포함하는 십진법 확장 및 집합이 포함되어 있습니다.

열 제목을 클릭하면 알파벳, 십진법 또는 집합별로 표를 정렬할 수 있습니다.오른쪽 란에 있는 기호들에 대한 설명은 그것들을 클릭하면 알 수 있습니다.

목록.

이름.	기호.	소수 확장	공식	연도	세트
하나.	1	1		선사시대	$\mathbb {N}$
두명	2	2		선사시대	$\mathbb {N}$
1/2	1/2	0.5		선사시대	$\mathbb {Q}$
파이	$\pi$	3.14159 26535 89793 23846 ^{[Mw 1]}^{[OEIS 1]}	원의 지름에 대한 원둘레의 비율.	기원전 1900년~1600년	$\mathbb {R} \setminus \mathbb {A}$
타우(수학 상수)	$\tau$	6.28318 53071 79586 47692^[3]^{[OEIS 2]}	원의 반지름에 대한 원둘레의 비율. $2\pi$ π $2\pi$ 에 해당합니다.	기원전 1900년~1600년	$\mathbb {R} \setminus \mathbb {A}$
2의 제곱근, 피타고라스 상수.^[4]	${\sqrt {2}$	1.41421 35623 73095 04880 ^{[Mw 2]}^{[OEIS 3]}	$x^{2}=2$ $x^{2}=2$ = $x^{2}=2$ ${\displaystyle x^{2$ }= $2}$ 의 양의 루트	기원전^[5] 1800년부터 1600년까지	$\mathbb {A}$
제곱근 3, 테오도로스 상수^[6]	${\sqrt {3}$	1.73205 08075 68877 29352 ^{[Mw 3]}^{[OEIS 4]}	$x^{2}=3$ $x^{2}=3$ = $x^{2}=3$ ${\displaystyle x^{2$ }= $3}$ 의 양의 루트	기원전 465년 ~ 기원전 398년	$\mathbb {A}$
제곱근 5^[7]	${\sqrt {5}$	2.23606 79774 99789 69640 ^{[OEIS 5]}	$x^{2}=5$ $x^{2}=5$ = $x^{2}=5$ ${\displaystyle x^{2$ }= $5}$ 의 양의 루트		$\mathbb {A}$
파이, 황금비^[8]	$\varphi$ $\phi$ {\ $displaystyle \varphi$ } $\varphi$ 또는 $\phi$ {\ $displaystyle \phi$ }	1.61803 39887 49894 84820 ^{[Mw 4]}^{[OEIS 6]}	${\frac {1+{\sqrt {5}}}{2}$	~300 BCE	$\mathbb {A}$
은비^[9]	$\delta _{S$	2.41421 35623 73095 04880 ^{[Mw 5]}^{[OEIS 7]}	${\sqrt {2}}+1$	~300 BCE	$\mathbb {A}$
영	0	0		기원전^[10] 300년~100년	$\mathbb {Z}$
네거티브 원	−1	−1		기원전 300~200년	$\mathbb {Z}$
2의 세제곱근	${\sqrt[{3}}{2}}$	1.25992 10498 94873 16476 ^{[Mw 6]}^{[OEIS 8]}	$x^{3}=2$ $x^{3}=2$ = $x^{3}=2$ ${\displaystyle x^{3$ }= $2}$ 의 실제 루트	46 ~ 120 CE^[11]	$\mathbb {A}$
3의 입방체근	${\sqrt[{3}}{3}}$	1.44224 95703 07408 38232 ^{[OEIS 9]}	$x^{3}=3$ $x^{3}=3$ = $x^{3}=3$ ${\displaystyle x^{3$ }= $3}$ 의 실제 루트		$\mathbb {A}$
2의 열두번째^[12]	${\sqrt[{12}}{2}}$	1.05946 30943 59295 26456 ^{[OEIS 10]}	$x^{12}=2$ $x^{12}=2$ = $x^{12}=2$ ${\displaystyle x^{12$ }= $2}$ 의 실제 루트		$\mathbb {A}$
초황금비^[13]	$\psi$	1.46557 12318 76768 02665 ^{[OEIS 11]}	${\frac {1+{\sqrt{3}}{\frac {29+3{\sqrt{93}}{2}}}}+{\sqrt[{3}}{\frac {29-3{\sqrt{93}}}{2}}}{3}}}$ $x^{3}=x^{2}+1$ $x^{3}=x^{2}+1$ = x $x^{3}=x^{2}+1$ + 1 ${\displaystyle$ x $^{3$ }= x $^{2}$ + $1}$ 의 실제 루트		$\mathbb {A}$
허수 단위^[14]	$i$	$0 + 1 i$	$x^{2}=-1$ $x^{2}=-1$ = - $x^{2}=-1$ ${\displaystyle x^{2$ }=- $1}$ 의 두 루트 중 하나입니다.	1501 ~ 1576	$\mathbb {C}$
육각형 격자의^[15]^[16] 연결 상수	$\mu$	1.84775 90650 22573 51225 ^{[Mw 7]}^{[OEIS 12]}	${\sqrt {2+{\sqrt {2}}}}$ + ${\sqrt {2+{\sqrt {2}}}}$ ${\displaystyle {\sqrt {2+{\sqrt {2}}},$ 다항식 $x^{4}-4x^{2}+2=0$ 4 - $x^{4}-4x^{2}+2=0$ $x^{4}-4x^{2}+2=0$ ${\sqrt {2+{\sqrt {2}}}}$ $x^{4}-4x^{2}+2=0$ + $x^{4}-4x^{2}+2=0$ $=$ $x^{4}-4x^{2}+2=0$ ${\displaystyle$ x $^{4}$ - $4x^{2$ ${\sqrt {2+{\sqrt {2}}}}$ + 2 = 0 $}$	1593^{[OEIS 12]}	$\mathbb {A}$
케플러-바우캄프 상수^[17]	$K'$	0.11494 20448 53296 20070 ^{[Mw 8]}^{[OEIS 13]}	$\prod _{n=3}^{\infty}}\cos \left ({\frac {\pi}{n}}\right)=\cos \left ({\frac {\pi}{3}\right)\cos \left ({\frac {\pi}{4}\right)\cos \left ({\frac {\pi}{5}\right)...$	1596^{[OEIS 13]}
월리스 상수		2.09455 14815 42326 59148 ^{[Mw 9]}^{[OEIS 14]}	${\sqrt[{3}]{\frac {45-{\sqrt {1929}}{18}}}+{\sqrt[{3}}{\frac {45+{\sqrt {1929}}{18}}}}$ $x^{3}-2x-5=0$ $x^{3}-2x-5=0$ - $x^{3}-2x-5=0$ 2 $x^{3}-2x-5=0$ - $x^{3}-2x-5=0$ = 0 ${\displaystyle$ x $^{3}-2x-5$ = $0}$ 의 실제 루트	1616년 ~ 1703년	$\mathbb {A}$
오일러 수^[18]	${\displaystylee}$	2.71828 18284 59045 23536 ^{[Mw 10]}^{[OEIS 15]}	$\lim _{n\to \infty}\left(1+{\frac {1}{n}}\right)^{n}=\sum _{n=0}^{\infty}{\frac {1}{n!}}=1+{\frac {1}{1!}}}+{\frac {1}{2!}}}+{\frac {1}{3!}}\cdots$	1618^[19]	$\mathbb {R} \setminus \mathbb {A}$
자연로그 2^[20]	$\ln 2$	0.69314 71805 59945 30941 ^{[Mw 11]}^{[OEIS 16]}	$e^{x}=2$ = $e^{x}=2$ ${\displaystyle$ e $^{x$ }= $2}$ 의 실제 루트 $\sum _{n=1}^{\infty}{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}{2}}+{\frac {1}{3}-{\frac {1}{4}}+\cdots$	1619 ^[21] & 1668^[22]	$\mathbb {R} \setminus \mathbb {A}$
렘니세이트 상수^[23]	$\varpi$	2.62205 75542 92119 81046 ^{[Mw 12]}^{[OEIS 17]}	$\pi \,{G}=4{\sqrt {2}{\pi}}\,\Gamma {\left ({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\pi}}\,\Gamma {\left ({\tfrac {1}{4}\right)^2}}$ 여기서 $G$ $G$ 는 $G$ 가우스 상수입니다.	1718년 ~ 1798년	$\mathbb {R} \setminus \mathbb {A}$
오일러 상수	$\gamma$	0.57721 56649 01532 86060 ^{[Mw 13]}^{[OEIS 18]}	$\lim _{n\to \infty}\left (-\log n+\sum _{k=1}^{n}{\frac {1}{k}}\right)=\int _{1}^{\infty}\left (-{\frac {1}{x}}+{\frac {1}{\lfloor x\rfloor}}\right), dx$	1735
에르드 ő스-보르바인 상수^[24]	$E$	1.60669 51524 15291 76378 ^{[Mw 14]}^{[OEIS 19]}	$\sum _{n=1}^{\infty}{\frac {1}{2^{n}-1}}={\frac {1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!\cdots$	1749^[25]	$\mathbb {R} \setminus \mathbb {Q$
오메가 상수	$\Omega$	0.56714 32904 09783 87299 ^{[Mw 15]}^{[OEIS 20]}	$W(1)={\frac {1}{\pi}}\int_{0}^{\pi}\log \left(1+{\frac {\sin t}{t}}e^{t\cot t}\right)dt$ 여기서 W는 램버트 W 함수입니다.	1758 & 1783	$\mathbb {R} \setminus \mathbb {A}$
아페리 상수^[26]	$\zeta(3)$	1.20205 69031 59594 28539 ^{[Mw 16]}^{[OEIS 21]}	$\sum _{n=1}^{\infty}{\frac {1}{n^{3}}={\frac {1}{1^{3}}+{\frac {1}{2^{3}}+{\frac {1}{3}}+{\frac {1}{4^{3}}+{\frac {1}{5^{3}}+\cdots$	1780^{[OEIS 21]}	$\mathbb {R} \setminus \mathbb {Q$
라플라스 한계^[27]		0.66274 34193 49181 58097 ^{[Mw 17]}^{[OEIS 22]}	${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ + ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ + ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ + ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ = ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$ ${\displaystyle {\frac {xe^{\sqrt {x^{2}+1}}{{\sqrt {x^{2}+1$ }}}{\sqrt {x^{2}+1 $}}$ = $1}$	~1782	$\mathbb {R} \setminus \mathbb {A}$
라마누잔 솔더 상수^[28]^[29]	$\mu$	1.45136 92348 83381 05028 ^{[Mw 18]}^{[OEIS 23]}	$\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ ( $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ ) $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ ⁡ $\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ = 0 ${\displaystyle \mathrm {l$ )=\ $int _{0}^{x}{\frac {dt}{\l$ t}}= $0$ 로그 적분 함수의 루트입니다.	1792^{[OEIS 23]}
가우스 상수^[30]	$G$	0.83462 68416 74073 18628 ^{[Mw 19]}^{[OEIS 24]}	${\frac {1}{\mathrm {agm}(1, {\sqrt {2}}}}={\frac {\Gamma}({\frac {1}{4}}^{2}}}}={\frac {2}{\pi }}\int_{0}^{1}{\frac {dx}{\sqrt {1-x^{4}}}}}:{\frac {1-x}}$ 여기서 agm은 산술 평균 – geometric 평균입니다.	1799^[31]	$\mathbb {R} \setminus \mathbb {A}$
헤르마이트 제2상수^[32]	$\gamma_{2}$	1.15470 05383 79251 52901 ^{[Mw 20]}^{[OEIS 25]}	${\frac {2}{\sqrt {3}}}$	1822년부터 1901년까지	$\mathbb {A}$
리우빌 상수^[33]	$L$	0.11000 10000 00000 00000 0001 ^{[Mw 21]}^{[OEIS 26]}	$\sum _{n=1}^{\infty}{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots$	1844년 이전	$\mathbb {R} \setminus \mathbb {A}$
최초 연속 분율 상수	$C_{1}$	0.69777 46579 64007 98201 ^{[Mw 22]}^{[OEIS 27]}	${\tfrac {1}{1+{\tfrac {1}{2+{\tfrac {1}{3+{\tfrac {1}{4+{\tfrac {1}{5+\cdots}}}}}}}}}}}.$ ${\$ ${I_{0}(2)}}.$ 여기서 $I_{\alpha }(x)$ $I_{\alpha }(x)$ ( $I_{\alpha }(x)$ $I_{\alpha}(x)$ 은 $I_{\alpha }(x)$ (는) 수정된 베셀 함수입니다.	1855^[34]	$\mathbb {R} \setminus \mathbb {Q$
라마누잔 상수^[35]		262 53741 26407 68743 .99999 99999 99250 073 ^{[Mw 23]}^{[OEIS 28]}	$e^{\pi {\sqrt {163}}}$	1859	$\mathbb {R} \setminus \mathbb {A}$
글라이셔-킨켈린 상수	$A$	1.28242 71291 00622 63687^{[Mw 24]}^{[OEIS 29]}	$e^{{\frac {1}{12}}-\zeta^{\prime }(-1)}=e^{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty}}{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left (-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)$	1860^{[OEIS 29]}
카탈루냐 상수^[36]^[37]^[38]	$G$	0.91596 55941 77219 01505 ^{[Mw 25]}^{[OEIS 30]}	$\int_{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {dx\,dy}{1{+}x^{2}y^{2}}=\!\sum _{n=0}^{\infty}\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}\!=\!{\frac {1}{1^{2}}{-}{\frac {1}{3^{2}}{+}{\cdots}}$	1864
도티 번호^[39]		0.73908 51332 15160 64165 ^{[Mw 26]}^{[OEIS 31]}	$\cos x=x$ ⁡ $\cos x=x$ = x ${\displaystyle \cos$ x = $x}$ 의 실제 루트	1865^{[Mw 26]}	$\mathbb {R} \setminus \mathbb {A}$
미셀-메르텐 상수^[40]	$M$	0.26149 72128 47642 78375 ^{[Mw 27]}^{[OEIS 32]}	$\lim _{n\to \infty}\left(\sum _{p\leq n}{\frac {1}{p}}-\ln \ln n\right)=\gamma +\sum _{p}\left(\ln \left(1-{\frac {1}{p}\right)+{\frac {1}{p}\right)$ 여기서 γ는 오일러-마스케로니 상수이고 p는 소수입니다.	1866 & 1873
보편 포물선 상수^[41]	$P$	2.29558 71493 92638 07403 ^{[Mw 28]}^{[OEIS 33]}	$\ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operator name {arsinh}(1)+{\sqrt {2}$	1891년^[42] 이전	$\mathbb {R} \setminus \mathbb {A}$
카헨 상수^[43]	$C$	0.64341 05462 88338 02618 ^{[Mw 29]}^{[OEIS 34]}	${\displaystyle \sum _{k=1}^{\infty}{\frac {(-1)^{k}}{{s_{k}-1}}={\frac {1}{2}}+{\frac {1}{6}}+{\frac {1}{42}}+{\frac {1}{1806}{,\pm \cdots}}}.$ 여기서 s는_k 실베스터 수열 2, 3, 7, 43, 1807의 k번째 항...	1891	$\mathbb {R} \setminus \mathbb {A}$
겔폰드 상수^[44]	$e^{\pi}$	23.14069 26327 79269 0057 ^{[Mw 30]}^{[OEIS 35]}	${\displaystyle(-1)^{-i}=i^{-2i}=\sum _{n=0}^{\infty}{\frac {\pi ^{n}}{n!}}=1+{\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2}}+{\frac {\pi ^{3}}{6}}+\cdots }$	1900^[45]	$\mathbb {R} \setminus \mathbb {A}$
겔폰드-슈나이더 상수^[46]	$2^{\sqrt {2}$	2.66514 41426 90225 18865 ^{[Mw 31]}^{[OEIS 36]}		1902년^{[OEIS 36]} 이전	$\mathbb {R} \setminus \mathbb {A}$
제2파바르 상수^[47]	$K_{2}$	1.23370 05501 36169 82735 ^{[Mw 32]}^{[OEIS 37]}	${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty}{\frac {1}{(2n-1)^{2}}}={\frac {1}{3^{2}}+{\frac {1}{5^{2}}+{\frac {1}{7^{2}}+\cdots$	1902년부터 1965년까지	$\mathbb {R} \setminus \mathbb {A}$
골든 앵글^[48]	$g$	2.39996 32297 28653 32223 ^{[Mw 33]}^{[OEIS 38]}	${\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})$ φ ${\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})$ $=$ π ${\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})$ - ${\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})$ ) ${\displaystyle {\frac {2\pi}{\varph$ }}=\ $pi(3$ - ${\sqrt {5}})$ 또는 $180(3-{\sqrt {5}})=137.50776\ldots$ - $180(3-{\sqrt {5}})=137.50776\ldots$ ) $=$ $180(3-{\sqrt {5}})=137.50776\ldots$ … ${\displaystyle 180(3$ - ${\sqrt {$ 5 $180(3-{\sqrt {5}})=137.50776\ldots$ }) = $137.50776\ldots }($ 도)	1907	$\mathbb {R} \setminus \mathbb {A}$
시에르피 ń스키 상수^[49]	$K$	2.58498 17595 79253 21706 ^{[Mw 34]}^{[OEIS 39]}	${\begin{aligned}&\pi \left(2\gamma +\ln{4}}{\frac {4}}^{4}}\right)=\pi(2\gamma +4\ln \Gamma({\tfrac {3}{4}})-\ln \pi )\&=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma(\tfrac {1}{4})\right)\end{aligned}$	1907
란다우-라마누잔 상수^[50]	$K$	0.76422 36535 89220 66299 ^{[Mw 35]}^{[OEIS 40]}	${\frac {1}{\sqrt {2}}\prod {{p\equiv 3}\text{mod}}4}\atop p\;{\rm {prime}}{\left(1-{\frac {1}{p^{2}}\right)^{-{\frac {1}{2}}}\!\!={\frac {\pi}{4}}\prod _{p\equiv 1{\text{mod}}4} \atop p\;{\rm {prime}}{\left(1-{\frac {1}{p^{2}}\right)^{\frac {1}{2}}$	1908^{[OEIS 40]}
닐슨-라마누잔 상수^[51]	$a_{1}$	0.82246 70334 24113 21823 ^{[Mw 36]}^{[OEIS 41]}	${\frac {\zeta}(2)}{2}}={\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty}}{\frac {(-1)^{n+1}}{n^{2}}={\frac {1}{1^{2}}{-}{\frac {1}{3^{2}}{-}{\frac {1}{4^{2}}{+}}{cdots$	1909	$\mathbb {R} \setminus \mathbb {A}$
기셰킹 상수^[52]	$G$	1.01494 16064 09653 62502 ^{[Mw 37]}^{[OEIS 42]}	${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty}}{\frac {1}{(3n+2)^{2}}+\sum _{n=1}^{\infty}{\frac {1}{(3n+1)^{2}}}\right)=$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ ( $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ - $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ + 1 $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ - $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ 5 $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ + $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ 2 $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ - 1 $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ 2 $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ + 1 $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ 2 ± $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ ) ${\displaystyle {\frac {3}}{{\sqrt {3}}{4}}\left$ frac { $1}{4^{2}}-{\frac {1}{7^{2}}+{\frac {1}{8^{2}}+{\frac {1}{10^{2}}\pm \cdots \right)}.$	1912
번스타인 상수^[53]	$\beta$	0.28016 94990 23869 13303 ^{[Mw 38]}^{[OEIS 43]}	$\lim _{n\to \infty }2nE_{2n}(f)$ n $\lim _{n\to \infty }2nE_{2n}(f)$ $\lim _{n\to \infty }2nE_{2n}(f)$ $\lim _{n\to \infty }2nE_{2n}(f)$ $\lim _{n\to \infty }2nE_{2n}(f)$ E $\lim _{n\to \infty }2nE_{2n}(f)$ $\lim _{n\to \infty }2nE_{2n}(f)$ ( $\lim _{n\to \infty }2nE_{2n}(f)$ f $\lim _{n\to \infty }2nE_{2n}(f)$ ) ${\displaystyle \lim _{n\to \infty}2nE_{2n}(f)},$ 여기서 E(f)는 구간 [-1, 1] 위의 실제 함수 f(x)에 대한 최량의 균일 근사 오차를 n 이하의 실수 다항식으로, $\lim _{n\to \infty }2nE_{2n}(f)$ (x) = x	1913
트리보나치 상수^[54]		1.83928 67552 14161 13255 ^{[Mw 39]}^{[OEIS 44]}	${\textstyle {\frac {1+{\sqrt[{3}}}{19+3{\sqrt{33}}}}+{\sqrt[{3}}{19-3{\sqrt{33}}}}{3}}={\frac {1+4\cosh \left ({\frac {1}{3}\cosh ^{-1}\left(2+{\frac {3}{8}}\right)\right){3}}}{3}}}}$ $x^{3}-x^{2}-x-1=0$ $x^{3}-x^{2}-x-1=0$ - $x^{3}-x^{2}-x-1=0$ $x^{3}-x^{2}-x-1=0$ - $x^{3}-x^{2}-x-1=0$ - $x^{3}-x^{2}-x-1=0$ = 0 ${\displaystyle x^{3}-x^{2}-x-1$ = $0}$ 의 실제 루트	1914년부터 1963년까지	$\mathbb {A}$
브룬 상수^[55]	$B_{2}$	1.90216 05831 04 ^{[Mw 40]}^{[OEIS 45]}	$\textstyle {\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+2}})}= ({\frac {1}{3}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}}) +\cdots$ p + 2가 역시 소수가 될 정도로 합이 모든 소수 p에 걸쳐 있는 경우	1919^{[OEIS 45]}
쌍대 소수 상수	$C_{2}$	0.66016 18158 46869 57392 ^{[Mw 41]}^{[OEIS 46]}	$\prod _{\textstyle {p\;{\rm {prime}} \atop p\geq 3}}\left(1-{\frac {1}{(p-1)^{2}}\right)$	1922
가소번호^[56]	$\rho$	1.32471 79572 44746 02596 ^{[Mw 42]}^{[OEIS 47]}	${\displaystyle {\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots}}}}}=\textstyle {\sqrt[{3}}{{\frac {1}{2}}}+{\frac {\sqrt {69}}}}+{\sqrt[{3}}{{\frac {1}{2}}-{\frac {\sqrt {69}}}}}.$ $x^{3}=x+1$ $x^{3}=x+1$ = x $x^{3}=x+1$ + $x^{3}=x+1$ ${\displaystyle x^{3$ }= $x+1}$ 의 실제 루트	1924^{[OEIS 47]}	$\mathbb {A}$
블로흐 상수^[57]	$B$	$0.4332\leq B\leq 0.4719$ ^{[Mw 43]}^{[OEIS 48]}	가장 잘 알려진 경계는 ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ + ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ × ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ - ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ - ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ⋅ γ (13 ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ) ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ γ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ γ ( ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ) ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ γ ( ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$ ) $displaystyle$ {\frac {\ $sqrt$ { $3}}{4}+2\times 10$ ^{-4 $}\leq B\leq$ {\ $sqrt$ {\ $frac {3}}-1}{2}\cdot {\frac {\frac$ { $1}{3}}\cdot$ {\frac ${\$ frac { $11}{12}}{\$ frac ${1}}}{\frac {4}}}$	1925^{[OEIS 48]}
97.5 퍼센트 포인트에 대한 Z 점수^[58]^[59]^[60]^[61]	$z_{.975}$	1.95996 39845 40054 23552 ^{[Mw 44]}^{[OEIS 49]}	${\sqrt {2}}\operatorname {erf} ^{-1}(0.95)$ ${\sqrt {2}}\operatorname {erf} ^{-1}(0.95)$ - ${\sqrt {2}}\operatorname {erf} ^{-1}(0.95)$ ( ${\sqrt {2}}\operatorname {erf} ^{-1}(0.95)$ ${\sqrt {2}}\operatorname {erf}^{-1}(0.95)$ 여기서 $erf(x)$ 는 역오류 함수입니다. ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ π ∫ - ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ ∞ z - ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ / ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ d ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ = ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$ ${\frac {1}{\sqrt {2\pi}}\int _{-\infty}^{z}e^{-x^{2}/2}\,\mathrm {d$ x = $0.975}$ 이(가) 되도록 실수 z $z$	1925
란다우 상수^[57]	$L$	$0.5<L\leq 0.54326$ ^{[Mw 45]}^{[OEIS 50]}	가장 잘 알려진 한계는 $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$ < $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$ $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$ γ γ $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$ ) $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$ γ γ $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$ ) ${\displaystyle 0.5$ < $L\leq {\frac {1}{3}}\Gamma({\frac {5}{6}}}{\Gamma({\frac {1}{6$ }}}}{\frac {1 $}}}}$ 입니다.	1929
란다우의 제3 상수^[57]	$A$	${\displaystyle 0.5<A\leq 0.7853>$		1929
프라우헤트-튜-모스 상수^[62]	$\tau$	0.41245 40336 40107 59778 ^{[Mw 46]}^{[OEIS 51]}	$\sum _{n=0}^{\infty}{\frac {t_{n}}{2^{n+1}}={\frac {1}{4}}\left[2-\prod_{n=0}^{\infty}}\left(1-{\frac {1}{2^{n}}}\right)\right]$ 여기서 ${t_{n}}$ ${\$ 는 ${t_{n}}$ Thue-Morse 수열의 n항입니다^th.	1929^{[OEIS 51]}	$\mathbb {R} \setminus \mathbb {A}$
골롬-딕만 상수^[63]	$\lambda$	0.62432 99885 43550 87099 ^{[Mw 47]}^{[OEIS 52]}	$\int _{0}^{1}e^{\mathrm {Li}(t)}dt=\int _{0}^{\infty}}{\frac {\rho(t)}{t+2}}dt$ 여기서 Li(t)는 로그 적분이고, ρ(t)는 딕맨 함수입니다.	1930 & 1964
르베그 상수의^[64] 점근적 거동과 관련된 상수	$c$	0.98943 12738 31146 95174 ^{[Mw 48]}^{[OEIS 53]}	$\lim _{n\to \infty}\!\left(\!{L_{n}{-}{\frac {4}{\pi^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi^{2}}\!\left ({\sum _{k=1}^{\infty}\!{\frac {2\lnk}{4k^{2}{-}1}}{-}}{\frac {\Gamma'({\tfrac {1}{2}})}{\Gamma({\tfrac {1}{2}}}}\!\!\right)$	1930^{[Mw 48]}
펠러-토르니에 상수^[65]	${\mathcal {C}}_{\mathrm {FT}$	0.66131 70494 69622 33528 ^{[Mw 49]}^{[OEIS 54]}	${{\frac {1}{2}}\prod _{p{\text {prime}}\left(1-{\frac {2}{p^{2}}\right)+{\frac {1}{2}}={\frac {3}{\pi ^{2}}\left(1-{\frac {1}{p^{2}-1}\right)+{\frac {1}$	1932
베이스 10 챔퍼노운 상수^[66]	$C_{10}$	0.12345 67891 01112 13141 ^{[Mw 50]}^{[OEIS 55]}	연속적인 정수의 표현을 연결하여 정의: 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...	1933	$\mathbb {R} \setminus \mathbb {A}$
세일럼 상수^[67]	$\sigma_{10}$	1.17628 08182 59917 50654 ^{[Mw 51]}^{[OEIS 56]}	$x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ + $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ - $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ x $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ - x $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ - x $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ - x $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ - $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ + $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ + x + $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ = $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$ ${\displaystyle$ x $^{10}$ + $x^{9}$ - x $^{7}$ - $x^{6}$ - $x^{5}$ - $x^{4}$ - $x^{3}$ + $x+1$ = $0}$	1933^{[OEIS 56]}	$\mathbb {A}$
킨친 상수^[68]	$K_{0}$	2.68545 20010 65306 44530 ^{[Mw 52]}^{[OEIS 57]}	$\prod _{n=1}^{\infty}}\left[{1+{1 \over n(n+2)}}\right]^{\log _{2}(n)}$	1934
레비 상수 (1)^[69]	$\beta$	1.18656 91104 15625 45282 ^{[Mw 53]}^{[OEIS 58]}	${\frac {\pi^{2}}{12\,\ln2}$	1935
레비 상수 (2)^[70]	$e^{\beta }$	3.27582 29187 21811 15978 ^{[Mw 54]}^{[OEIS 59]}	$e^{\pi ^{2}/(12\ln 2)}$	1936
코프랜드-에르드 ő 상수^[71]	${\mathcal {C}}_{CE$	0.23571 11317 19232 93137 ^{[Mw 55]}^{[OEIS 60]}	연속적인 소수의 표현을 연결하여 정의: 0.2 3 5 7 11 13 17 19 23 29 31 37 ...	1946^{[OEIS 60]}	$\mathbb {R} \setminus \mathbb {Q$
밀스 상수^[72]	$A$	1.30637 78838 63080 69046 ^{[Mw 56]}^{[OEIS 61]}	⌊ $\lfloor A^{3^{n}}\rfloor$ A $\lfloor A^{3^{n}}\rfloor$ $\lfloor A^{3^{n}}\rfloor$ ⌋ ${\displaystyle$ \ $lfloor$ A $^{3^{n}}\rfloor$ }이 $($ 가) 모든 양의 정수 n에 대해 소수일 때 가장 작은 양의 실수 A	1947
곰페르츠 상수^[73]	$\delta$	0.59634 73623 23194 07434 ^{[Mw 57]}^{[OEIS 62]}	${\displaystyle \int_{0}^{\infty}\!\!{\frac {e^{-x}}{1+x}}\, dx=\!\!\int_{0}^{1}\!\!{\frac {dx}{1-\ln x}}={\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {2}{1+{\tfrac {2}{1+{\tfrac {3}{1+3{/\cdots}}}}}}}}}.$	1948년^{[OEIS 62]} 이전
드 브루인-뉴먼 상수	$\Lambda$	$0\leq \Lambda \leq 0.2$	$H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ λ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ = ∫ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ ∞ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ λ u $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ φ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ ⁡ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ ${\displaystyle$ H $(\lambda,z$ )=\ $int$ _ ${0}^{\infty }e^{\$ lambda $u^{2}}\Phi(u)\cos(zu)du}$ 의 경우 λ ≥ λ인 경우에만 실수 0을 갖습니다. 여기서 φ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ ( $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ ) $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ = ∑ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ = $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ ∞ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ π $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ n $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ 9 $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ - $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ π $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ 2 $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ ) e - $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ π $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$ ${\displaystyle \Phi(u$ )=\ $sum _{n$ = $1}^{\infty}(2\pi ^{2}^{9u}-3\pi n^{2}e^{5u})$ e $^{-\pi n^{$ 2 $e^{4u}}.$	1950
반데르 파우 상수	${\frac {\pi}{\ln2}$	4.53236 01418 27193 80962 ^{[OEIS 63]}		1958년^{[OEIS 64]} 이전	$\mathbb {R} \setminus \mathbb {Q$
요술각^[74]	$\theta _{\mathrm {m}}$	0.95531 66181 245092 78163 ^{[OEIS 65]}	$\arctan {\sqrt {2}}=\arccos {\tfrac {1}{\sqrt {3}}\approx \textstyle {54.7356}^{\circ}$	1959년^[75]^[74] 이전	$\mathbb {R} \setminus \mathbb {A}$
아르틴 상수^[76]	$C_{\mathrm {Artin}}$	0.37395 58136 19202 28805 ^{[Mw 58]}^{[OEIS 66]}	$\prod _{p{\text{prime}}\left(1-{\frac {1}{p(p-1)}}\right)$	1961년^{[OEIS 66]} 이전
포터 상수^[77]	$C$	1.46707 80794 33975 47289 ^{[Mw 59]}^{[OEIS 67]}	${\frac {6\ln 2}{\pi ^{2}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)'-{\frac {1}}$ 여기서 γ는 오일러-마스케로니 상수이고 ζ $'(2)$ 는 s = 2에서 평가된 리만 제타 함수의 도함수입니다.	1961^{[OEIS 67]}
로치 상수^[78]	$L$	0.97027 01143 92033 92574 ^{[Mw 60]}^{[OEIS 68]}	${\frac {6\ln2\ln10}{\pi^{2}}}$	1964
데비치의 시험관상수		1.00743 47568 84279 37609 ^{[OEIS 69]}	4D 하이퍼큐브에서 통과할 수 있는 가장 큰 큐브입니다. 4 $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ - $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ x $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ - $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ 7 $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ + $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ 2 $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ + $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ = $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$ ${\displaystyle 4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16$ = $0}$	1966^{[OEIS 69]}	$\mathbb {A}$
리브의 제곱 얼음 상수^[79]		1.53960 07178 39002 03869 ^{[Mw 61]}^{[OEIS 70]}	$\left ({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}$	1967	$\mathbb {A}$
니븐 상수^[80]	$C$	1.70521 11401 05367 76428 ^{[Mw 62]}^{[OEIS 71]}	$1+\sum _{n=2}^{\infty}}\left(1-{\frac {1}{\zeta(n))}\right)$	1969
스티븐스 상수^[81]		0.57595 99688 92945 43964 ^{[Mw 63]}^{[OEIS 72]}	$\prod _{p{\text{prime}}\left(1-{\frac {p}{p^{3}-1}}\right)$	1969^{[OEIS 72]}
정기적인 종이접기^[82]^[83]	$P$	0.85073 61882 01867 26036 ^{[Mw 64]}^{[OEIS 73]}	${\displaystyle \sum _{n=0}^{\infty}{\frac {8^{2^{n}}}{2^{n+2}}-1}}=\sum _{n=0}^{\infty}{\tfrac {1}{2^{n}}}{1-{\tfrac {1}{2^{n+2}}}}}.$	1970^{[OEIS 73]}	$\mathbb {R} \setminus \mathbb {A}$
역수 피보나치 상수^[84]	$\psi$	3.35988 56662 43177 55317 ^{[Mw 65]}^{[OEIS 74]}	$\sum _{n=1}^{\infty}{\frac {1}{F_{n}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ 여기서 F는_n n 피보나치 수이다^th.	1974^{[OEIS 74]}	$\mathbb {R} \setminus \mathbb {Q$
이진 알파벳에 대한 Chvátal-Sankoff 상수	$\gamma_{2}$	$0.788071\leq \gamma _{2}\leq 0.826280$	$\lim _{n\to \infty}{\frac {\operatorname {E}[\lambda _{n,2}}{n}}$ 여기서 $E[$ λ $]$ 는 두 개의 임의 길이-n 이진 문자열의 예상되는 가장 긴 공통 연속입니다.	1975
파이겐바움 상수	$\delta$	4.66920 16091 02990 67185 ^{[Mw 66]}^{[OEIS 75]}	$\lim _{n\to \infty}{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}$ 여기서 수열 x는 $x_{n+1}=ax_{n}(1-x_{n})$ $x_{n+1}=ax_{n}(1-x_{n})$ + $x_{n+1}=ax_{n}(1-x_{n})$ = x $x_{n+1}=ax_{n}(1-x_{n})$ ( $x_{n+1}=ax_{n}(1-x_{n})$ - $x_{n+1}=ax_{n}(1-x_{n})$ ) ${\displaystyle$ x_{ $n+1}$ = $ax_{n}($ 1 - $x_{n})}$	1975
차이틴 상수 ^[86]	$\Omega$	일반적으로 그것들은 계산할 수 없는 수이다. 그런데 그런 숫자가 0.00787 49969 97812 3844입니다. ^{[Mw 67]}^{[OEIS 76]}	$\sum _{p\in P}2^{- p}$ $p$ : 중단된 프로그램 $p$ : 프로그램 $p$ 의 비트 단위 크기 $P$ : 중지되는 모든 프로그램의 도메인입니다. 참고 항목:중단문제	1975	$\mathbb {R} \setminus \mathbb {A}$
로빈스 상수^[87]	$\Delta(3)$	0.66170 71822 67176 23515 ^{[Mw 68]}^{[OEIS 77]}	${\frac {4\!+\!17{\sqrt{2}}\!-6{\sqrt{3}}\!-7\pi}{105}\!+\!{\frac {\ln(1\)!+\!{\sqrt{2}}}{5}}\!+\!{\frac {2\ln(2\)!+\!{\sqrt{3}}}{5}$	1977^{[OEIS 77]}	$\mathbb {R} \setminus \mathbb {A}$
바이어슈트라스 상수		0.47494 93799 87920 65033 ^{[Mw 69]}^{[OEIS 78]}	${\frac {2^{5/4}{\sqrt {\pi}}\,e^{\pi /8}}{\Gamma({\frac {1}{4}})^{2}}$	1978년^[89] 이전	$\mathbb {R} \setminus \mathbb {A}$
프랑센-로빈슨 상수^[90]	$F$	2.80777 02420 28519 36522 ^{[Mw 70]}^{[OEIS 79]}	$\int _{0}^{\infty}{\frac {dx}{\Gamma(x)}}=e+\int _{0}^{\infty}{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\, dx$	1978
파이겐바움 상수^[91] α	$\alpha$	2.50290 78750 95892 82228 ^{[Mw 66]}^{[OEIS 80]}	분기 다이어그램에서 두 부분 라인의 너비와 너비 간의 비율	1979
부아레몽 상수 2차^[92]	$C_{2}$	0.19452 80494 65325 11361 ^{[Mw 71]}^{[OEIS 81]}	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty}}\left {{\frac {d}{dt}}\left ({\frac {\sin t}{t}\right)^{2}}\right \,dt-1$	1983^{[OEIS 81]}	$\mathbb {R} \setminus \mathbb {A}$
에르트 ő스-테넨바움-포드 상수	$\delta$	0.86071 33205 59342 06887 ^{[OEIS 82]}	$1-{\frac {1+\log \log 2}{\log 2}$	1984
콘웨이 상수^[93]	$\lambda$	1.30357 72690 34296 39125 ^{[Mw 72]}^{[OEIS 83]}	다항식의 실수근: ${\displaystyle {\begin{smallmatrix}}x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{58}+5x^{57}-3x^{56}-2x^{55}-10x^{54}-3x^{52}+6x^{51}+6x^{50}\++x^{48}-3x^{47}-7x^{46}-8x^{45}+10x^{43}+6x^{41}-5x^{40}\-12x^{39}+7x^{38}+7x^{36}+3x^{35}-3x^{33}+6x^{32}-6x^{3}1}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\0\quad \quad \end{smallmatrix}$	1987	$\mathbb {A}$
하프너-사르낙-맥컬리 상수^[94]	$\sigma$	0.35323 63718 54995 98454 ^{[Mw 73]}^{[OEIS 84]}	$\prod _{p{\text{prime}}{\left(1-\left(1-\prod _{n\geq 1})\left(1-{\frac {1}{p^{n}}\right)^{2}\right)}\!$	1991^{[OEIS 84]}
백하우스 상수^[95]	$B$	1.45607 49485 82689 67139 ^{[Mw 74]}^{[OEIS 85]}	$\lim _{k\to \infty}\left {\frac {q_{k+1}}{q_{k}}\right\vert \quad \scriptstyle {\text{where:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty}q_{k}x^{k}$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ ( $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ ) $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ + $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ p $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ = 1 $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ + $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ + $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ + 5 $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ + $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$ ⋯ ${\displaystyle P$ ) = 1 $+\sum$ }} = $1$ + 2 + $3x^{2}$ + $5x^{3}$ + \ $cdots }$ 여기서 p는 k 소수입니다.	1995
비스와나 상수^[96]		1.13198 82487 943 ^{[Mw 75]}^{[OEIS 86]}	$\lim _{n\to \infty }\|f_{n}\|^{\frac {1}{n}}$ $\lim _{n\to \infty }\|f_{n}\|^{\frac {1}{n}}$ $\lim _{n\to \infty }\|f_{n}\|^{\frac {1}{n}}$ $\lim _{n\to \infty }\|f_{n}\|^{\frac {1}{n}}$ $\lim _{n\to \infty }\|f_{n}\|^{\frac {1}{n}}$ $\lim _{n\to \infty} f_{n} ^{\frac {1}{n}}$ 여 $\lim _{n\to \infty }\|f_{n}\|^{\frac {1}{n}}$ 서 f = f ± f, 부호 + 또는 -가 동일한 확률로 임의로 선택됩니다.	1997
코모르니크-로레티 상수^[97]	$q$	1.78723 16501 82965 93301 ^{[Mw 76]}^{[OEIS 87]}	$1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ = ∑ $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ = $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ ∞ $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ ${\$ $displaystyle$ q} {\ $displaystyle$ q} {\displaystyle 1=\ $sum _{k$ = $1}^{\infty}{\frac {t_{k}}},$ 또는 $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$ ∏ $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ = 0 ∞ $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ ( $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ - $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ ) + $q$ - $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ - $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ = $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ ${\displaystyle \$ prod $_{n$ = $0}^{\infty}\left(1-{\frac {1}{q^{n}}\right)+{\frac {q-2}{q-1$ }}= $0}$ 여기서 t는_k Thue-Morse 수열의 k항입니다^th.	1998	$\mathbb {R} \setminus \mathbb {A}$
엠브리-트레페텐 상수	$\beta ^{\star}$	0.70258		1999
히스-브라운-모로 상수^[98]	$C$	0.00131 76411 54853 17810 ^{[Mw 77]}^{[OEIS 88]}	$\prod _{p{\text{prime}}\left(1-{\frac {1}{p}}\right)^{7}\left(1+{\frac {7p+1}{p^{2}}\right)$	1999^{[OEIS 88]}
MRB 상수^[99]^[100]^[101]	$S$	0.18785 96424 62067 12024 ^{[Mw 78]}^{[Ow 1]}^{[OEIS 89]}	$\sum _{n=1}^{\infty}(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots$	1999
극상수^[102]	$\rho$	0.41468 25098 51111 66024 ^{[OEIS 90]}	$\sum _{p{\text{prime}}}{\frac {1}{2^{p}}}={\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{32}}+\cdots}$	1999^{[OEIS 90]}	$\mathbb {R} \setminus \mathbb {Q$
소모스의 이차 재발 상수^[103]	$\sigma$	1.66168 79496 33594 12129 ^{[Mw 79]}^{[OEIS 91]}	$\prod _{n=1}^{\infty}}n^{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots$	1999^{[Mw 79]}
포이아스 상수^[104]	$\alpha$	1.18745 23511 26501 05459 ^{[Mw 80]}^{[OEIS 92]}	$x_{n+1}=\left(1+{\frac {1}{x_{n}}\right)^{n}{\text{for}}}n=1,2,3,\ldots$ foias 상수는 x = α인 경우 수열이 무한대로 발산되는 유일한 실수입니다.	2000
단위 디스크의^[105]^[106] 로그 용량		0.59017 02995 08048 11302 ^{[Mw 81]}^{[OEIS 93]}	${\frac {\tfrac {1}{4}}^{2}}{4\pi ^{3/2}}$	2003년^{[OEIS 93]} 이전	$\mathbb {R} \setminus \mathbb {A}$
다니구치 상수^[81]		0.67823 44919 17391 97803 ^{[Mw 82]}^{[OEIS 94]}	$\prod _{p{\text{prime}}\left(1-{\frac {3}{p^{3}}}+{\frac {2}{p^{4}}}+{\frac {1}{p^{5}}-{\frac {1}{p^{6}}\right)$	2005년^[81] 이전

표현에 따라 연속 분수로 정렬된 수학 상수

다음 목록에는 일부 상수의 연속 분수가 포함되어 있으며 이들의 표현에 따라 정렬됩니다.알려진 항이 20개를 초과하는 연속된 분수는 계속됨을 나타내는 타원과 함께 절단되었습니다.유리수는 두 개의 연속된 분수를 갖습니다. 이 목록의 버전은 더 짧은 버전입니다.소수점 표현은 값이 알려진 경우 반올림되거나 10자리로 패딩됩니다.

이름.	기호.	세트	소수 확장	연속분율	메모들
영	0	$\mathbb {Z}$	0.00000 00000	[0; ]
골롬-딕만 상수	$\lambda$		0.62432 99885	[0; 1, 1, 1, 1, 1, 22, 1, 2, 3, 1, 1, 11, 1, 1, 2, 22, 2, 6, 1, 1, …] ^{[OEIS 95]}	E. Weisstein은 계속되는 분수가 비정상적으로 많은 수의 1을 갖는다고 언급했습니다.^{[Mw 83]}
카헨 상수	$C_{2}$	$\mathbb {R} \setminus \mathbb {A}$	0.64341 05463	[0; 1, 1, 1, 2², 3², 13², 129², 25298², 420984147², 269425140741515486², …] ^{[OEIS 96]}	크기가 크기 때문에 모든 항이 정사각형이고 10개 항에서 잘립니다.Davison과 Shallit는 상수가 초월적이라는 것을 증명하기 위해 지속적인 분수 확장을 사용했습니다.
오일러-마스케로니 상수	$\gamma$		0.57721 56649^[107]	[0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, …] ^[107]^{[OEIS 97]}	$지속적$ 인 분율 확장을 사용하여 γ이 유리하면 분모가 10을 초과해야 함을 보여주었습니다.
최초 연속 분율 상수	$C_{1}$	$\mathbb {R} \setminus \mathbb {Q$	0.69777 46579	[0; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …]	2에서 평가된 첫 번째 종류의 수정된 베셀 함수의 비율 $I_{1}(2)/I_{0}(2)$ $I_{1}(2)/I_{0}(2)$ $I_{1}(2)/I_{0}(2)$ ( $I_{1}(2)/I_{0}(2)$ ) $I_{1}(2)/I_{0}(2)$ / $I_{1}(2)/I_{0}(2)$ $I_{1}(2)/I_{0}(2)$ $I_{1}(2)/I_{0}(2)$ ) ${\displaystyle I_{1}(2)$ / $I_{0}(2)}$ 와 같습니다.
카탈루냐 상수	$G$		0.91596 55942^[108]	[0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, …] ^[108]^{[OEIS 98]}	E가 최대 4851389025항을 계산했습니다.Weisstein.^{[Mw 84]}
1/2	1/2	$\mathbb {Q}$	0.50000 00000	[0; 2]
프라우헤트-튜-모스 상수	$\tau$	$\mathbb {R} \setminus \mathbb {A}$	0.41245 40336	[0; 2, 2, 2, 1, 4, 3, 5, 2, 1, 4, 2, 1, 5, 44, 1, 4, 1, 2, 4, 1, …] ^{[OEIS 99]}	무한히 많은 부분승수는 4 또는 5이고 무한히 많은 부분승수는 50보다 크거나 같습니다.^[109]
코프랜드-에르드 ő 상수	${\mathcal {C}}_{CE$	$\mathbb {R} \setminus \mathbb {Q$	0.23571 11317	[0; 4, 4, 8, 16, 18, 5, 1, 1, 1, 1, 7, 1, 1, 6, 2, 9, 58, 1, 3, 4, …] ^{[OEIS 100]}	E에 의해 최대 1011597392항을 계산했습니다.Weisstein.또한 Champernown 상수의 연속 분율은 산발적으로 큰 항을 포함하고 있지만 Copeland-Erd ő 상수의 연속 분율은 이러한 성질을 나타내지 않는다고 언급했습니다.
베이스 10 챔퍼노운 상수	$C_{10}$	$\mathbb {R} \setminus \mathbb {A}$	0.12345 67891	[0; 8, 9, 1, 149083, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 1, 15, 4.57540×10, 6¹⁶⁵, 1, …]	모든 기저에 있는 챔퍼노운 상수는 산발적으로 큰 수를 나타냅니다. C $C_{10}$ ${\$ 의 40번째 항은 2504자리입니다 $C_{10}$ .
하나.	1	$\mathbb {N}$	1.00000 00000	[1; ]
파이, 황금비	$\varphi$	$\mathbb {A}$	1.61803 39887^[110]	[1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …] ^[111]	수렴은 연속적인 피보나치 수의 비율입니다.
브룬 상수	$B_{2}$		1.90216 05831	[1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, …]	n개의^th 수렴자 분모의 n 근은^th 힌친 상수에 가까우며, 이는 $B_{2}$ ${\$ 가 비이성적임을 나타냅니다 $B_{2}$ .만약 사실이라면, 이것은 쌍둥이 소수의 추측을 증명할 것입니다.^[112]
2의 제곱근	${\sqrt {2}$	$\mathbb {A}$	1.41421 35624	[1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …]	수렴은 연속적인 Pell 수의 비율입니다.
두명	2	$\mathbb {N}$	2.00000 00000	[2; ]
오일러 수	${\displaystylee}$	$\mathbb {R} \setminus \mathbb {A}$	2.71828 18285^[113]	[2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, …] ^[114]^{[OEIS 102]}	지속적인 분율 확장은 [2; 1, 2, 1, 1, 4, 1, ..., 1, 2n, 1, ...] 패턴을 갖습니다.
킨친 상수	$K_{0}$		2.68545 20011^[115]	[2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, …] ^[116]^{[OEIS 103]}	거의 모든 실수 x에 대하여, x의 연속 분율의 계수는 킨친 상수로 알려진 유한한 기하평균을 갖습니다.
세개	3	$\mathbb {N}$	3.00000 00000	[3; ]
파이	$\pi$	$\mathbb {R} \setminus \mathbb {A}$	3.14159 26536	[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, …] ^{[OEIS 104]}	처음 몇 개의 수렴체(3, 22/7, 333/106, 355/113, ...)는 $가장$ 잘 알려져 있고 가장 널리 사용되는 π의 과거 근사치 중 하나입니다.

상수의 수열

이름.	기호.	공식	연도	세트
고조파수	$H_{n}$	$\sum _{k=1}^{n}{\frac {1}{k}$	고대	$\mathbb {Q}$
그레고리 계수	$G_{n}$	${\frac {1}{n!}}\int _{0}^{1}x(x-1)(x-1)(x-2)\cdots(x-n+1)\, dx=\int _{0}^{1}{\binom {x}{n}}\, dx$	1670	$\mathbb {Q}$
베르누이 수	$B_{n}^{\pm}$	${\frac {t}{2}}\left(\operator name {coth} {\frac {t}{2}}\pm 1\right)=\sum_{m=0}^{\infty}{\frac {B_{m}^{\pm {}t^{m}}{m!}}$	1689	$\mathbb {Q}$
헤르마이트 상수^[Mw86]	$\gamma_{n}$	유클리드 공간 R의 격자 L에 대해 단위 공량, 즉 vol(R/L) = 1인 경우, λ(L)이 L의 0이 아닌 요소의 최소 길이를 나타내도록 합니다.그러면 √γn은 모든 그러한 격자 L에 대하여 λ(L)의 최대치가 됩니다.	1822년부터 1901년까지	$\mathbb {R}$
하프너-사르낙-맥컬리 상수^[117]	$D(n)$	$D(n)=\prod _{k=1}^{\infty}\left\{1-\left[1-\prod_{j=1}^{n}(1-p_{k}^{-j})\right]^{2}\right\$	1883^{[Mw 87]}	$\mathbb {R}$
스틸제 상수	$\gamma_{n}$	${\frac {(-1)^{n}n!}{2\pi }}\int_{0}^{2\pi }e^{-nix}\zeta \left(e^{ix}+1\right) dx.$	1894년 이전에	$\mathbb {R}$
기호 상수^[47]^{[Mw 88]}	$K_{r}$	${\frac {4}{\pi}}\sum _{n=0}^{\infty}}\left ({\frac {(-1)^{n}}{2n+1}}\right)^{\!r+1}={\frac {4}{\pi}}\left ({\frac {(-1)^{0(r+1)}}+{\frac {(-1)^{1(r+1)}}}+{3^{r}}+{\frac {(-1)^{2(r+1)}}+{5^{r}}+{\frac {(-1)^{3(r+1)}}+{7^{r}}+\cdots \right)$	1902년부터 1965년까지	$\mathbb {R}$
일반화된 브룬 상수^[55]	$B_{n}$	${\displaystyle {$ $}}$ p + n이 또한 소수가 될 수 있도록 합이 모든 소수 p에 걸쳐 있는 경우 ${\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+n}})}$	1919^{[OEIS 45]}	$\mathbb {R}$
챔퍼노운 상수^[66]	$C_{b}$	연속 정수의 표현을 b 밑면에 연결하여 정의합니다. $C_{b}=\sum _{n=1}^{\infty}{\frac {n}{b^{\left(\sum _{k=1}^{n}\lceil \log _{b}(k+1)\rceil \rceil \right)}}}$	1933	$\mathbb {R} \setminus \mathbb {A}$
라그랑주수	$L(n)$	${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ - ${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ ${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ ${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ ${\displaystyle {\sqrt {$ 9 - ${\frac {4}{m_{n}}^{2}}}}.$ 여기서 $m_{n}$ $m_{n}$ 은 $m^{2}+x^{2}+y^{2}=3mxy\,$ + $m^{2}+x^{2}+y^{2}=3mxy\,$ $2$ ${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ y $m^{2}+x^{2}+y^{2}=3mxy\,$ $=$ $m^{2}+x^{2}+y^{2}=3mxy\,$ $m^{2}+x^{2}+y^{2}=3mxy\,$ $m^{2$ + ${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ $^{2}$ = 3 $mxy\}$ 중에서 n번째로 작은 수입니다.	1957년 이전에	$\mathbb {A}$
펠러의 동전 던지기 상수	$\alpha_{k},\beta_{k$	$\alpha _{k}$ $\alpha _{k}$ $\alpha_{k}$ 는 $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $\alpha _{k}$ + $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ + 1 $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ - 1 $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ ), $\alpha _{k}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ k = 2 $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ - $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ + 1 - $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$ ${\displaystyle$ x $^$ $\alpha _{k}$ $k+1$ }= $2^{k+1}(x$ $\alpha _{k}$ $\beta$ $\alpha _{k}$ _ ${k$ }= {\ $frac$ { $2-\alpha_{k}}{k+1-k\alpha_{k}}}$ 인 양의 실수근입니다.	1968	$\mathbb {A}$
스톤햄 수	$\alpha_{b,c}$	$\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ k $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ > $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ b $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ = $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ ∞ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ b $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ k $\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ {\ $displaystyle \su$ _{ $n=c^{k}>1}{\frac {1}{b^$ }}}=\ $su$ _{k $=1}^{\infty}}{\frac {1}{b^{c^{k}}c^{k}}{\$ frac {1}{b,c}}{b,c는 공모 정수입니다.	1973	$\mathbb {R} \setminus \mathbb {Q$
베라하 상수	$B(n)$	$2+2\cos \left ({\frac {2\pi}{n}}\right)$	1974	$\mathbb {A}$
슈바탈-산코프 상수	$\gamma _{k}$	$\lim _{n\to \infty}}{\frac {E[\lambda _{n,k}}}{n}$	1975	$\mathbb {R}$
하이퍼하모닉 넘버	$H_{n}^{(r)}$	$=$ $H_{k}^{(r-1)},$ $H_{n}^{(0)}={\frac {1}{n}}$ $=$ $H_{n}^{(0)}={\frac {1}{n}}$ ${\displaystyle H_{n}^{(0$ )} $=$ {\ $frac {1}{n}}}$	1995	$\mathbb {Q}$
그레고리 수	$G_{x}$	$\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ $=$ $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ 보다 큰 유리 x에 $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ 해 $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ ( $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ - $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ ) $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ ( $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ + $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ 1 ) x 2 n + 1 ${\displaystyle$ \su $\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ _{n=0 $}^{\infty}(-1)^{n}{\frac {1}{(2n$ +1) $x^{$ 2n $+1$ }}}}.	1996년 이전에	$\mathbb {R}$
금속평균		${\frac {n+{\sqrt {n^{2}+4}}}{2}}$	1998년 이전에	$\mathbb {A}$

참고 항목

메모들

^ $i$ 와 $-i$ 둘 다 이 방정식의 근이지만, 두 근 모두 대수적으로 동치이기 때문에 진정으로 "양의"이거나 다른 근보다 더 기본적이지 않습니다. $i$ 와 $-i$ 의 부호의 구별은 어떤 면에서는 임의적이지만 유용한 표기법 장치입니다.자세한 내용은 상상 단위를 참조하십시오.

참고문헌

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사이트 MathWorld Wolfram.com

^ Weisstein, Eric W. "Pi Formulas". MathWorld.
^ Weisstein, Eric W. "Pythagoras's Constant". MathWorld.
^ Weisstein, Eric W. "Theodorus's Constant". MathWorld.
^ Weisstein, Eric W. "Golden Ratio". MathWorld.
^ Weisstein, Eric W. "Silver Ratio". MathWorld.
^ Weisstein, Eric W. "Delian Constant". MathWorld.
^ Weisstein, Eric W. "Self-Avoiding Walk Connective Constant". MathWorld.
^ Weisstein, Eric W. "Polygon Inscribing". MathWorld.
^ Weisstein, Eric W. "Wallis's Constant". MathWorld.
^ Weisstein, Eric W. "e". MathWorld.
^ Weisstein, Eric W. "Natural Logarithm of 2". MathWorld.
^ Weisstein, Eric W. "Lemniscate Constant". MathWorld.
^ Weisstein, Eric W. "Euler–Mascheroni Constant". MathWorld.
^ Weisstein, Eric W. "Erdos-Borwein Constant". MathWorld.
^ Weisstein, Eric W. "Omega Constant". MathWorld.
^ Weisstein, Eric W. "Apéry's Constant". MathWorld.
^ Weisstein, Eric W. "Laplace Limit". MathWorld.
^ Weisstein, Eric W. "Soldner's Constant". MathWorld.
^ Weisstein, Eric W. "Gauss's Constant". MathWorld.
^ Weisstein, Eric W. "Hermite Constants". MathWorld.
^ Weisstein, Eric W. "Liouville's Constant". MathWorld.
^ Weisstein, Eric W. "Continued Fraction Constants". MathWorld.
^ Weisstein, Eric W. "Ramanujan Constant". MathWorld.
^ Weisstein, Eric W. "Glaisher-Kinkelin Constant". MathWorld.
^ Weisstein, Eric W. "Catalan's Constant". MathWorld.
^ ^a ^b Weisstein, Eric W. "Dottie Number". MathWorld.
^ Weisstein, Eric W. "Mertens Constant". MathWorld.
^ Weisstein, Eric W. "Universal Parabolic Constant". MathWorld.
^ Weisstein, Eric W. "Cahen's Constant". MathWorld.
^ Weisstein, Eric W. "Gelfonds Constant". MathWorld.
^ Weisstein, Eric W. "Gelfond-Schneider Constant". MathWorld.
^ Weisstein, Eric W. "Favard Constants". MathWorld.
^ Weisstein, Eric W. "Golden Angle". MathWorld.
^ Weisstein, Eric W. "Sierpinski Constant". MathWorld.
^ Weisstein, Eric W. "Landau-Ramanujan Constant". MathWorld.
^ Weisstein, Eric W. "Nielsen-Ramanujan Constants". MathWorld.
^ Weisstein, Eric W. "Gieseking's Constant". MathWorld.
^ Weisstein, Eric W. "Bernstein's Constant". MathWorld.
^ Weisstein, Eric W. "Tribonacci Constant". MathWorld.
^ Weisstein, Eric W. "Brun's Constant". MathWorld.
^ Weisstein, Eric W. "Twin Primes Constant". MathWorld.
^ Weisstein, Eric W. "Plastic Constant". MathWorld.
^ Weisstein, Eric W. "Bloch Constant". MathWorld.
^ Weisstein, Eric W. "Confidence Interval". MathWorld.
^ Weisstein, Eric W. "Landau Constant". MathWorld.
^ Weisstein, Eric W. "Thue-Morse Constant". MathWorld.
^ Weisstein, Eric W. "Golomb-Dickman Constant". MathWorld.
^ ^a ^b Weisstein, Eric W. "Lebesgue Constants". MathWorld.
^ Weisstein, Eric W. "Feller-Tornier Constant". MathWorld.
^ Weisstein, Eric W. "Champernowne Constant". MathWorld.
^ Weisstein, Eric W. "Salem Constants". MathWorld.
^ Weisstein, Eric W. "Khinchin's Constant". MathWorld.
^ Weisstein, Eric W. "Levy Constant". MathWorld.
^ Weisstein, Eric W. "Levy Constant". MathWorld.
^ Weisstein, Eric W. "Copeland-Erdos Constant". MathWorld.
^ Weisstein, Eric W. "Mills Constant". MathWorld.
^ Weisstein, Eric W. "Gompertz Constant". MathWorld.
^ Weisstein, Eric W. "Artin's Constant". MathWorld.
^ Weisstein, Eric W. "Porter's Constant". MathWorld.
^ Weisstein, Eric W. "Lochs' Constant". MathWorld.
^ Weisstein, Eric W. "Liebs Square Ice Constant". MathWorld.
^ Weisstein, Eric W. "Niven's Constant". MathWorld.
^ Weisstein, Eric W. "Stephen's Constant". MathWorld.
^ Weisstein, Eric W. "Paper Folding Constant". MathWorld.
^ Weisstein, Eric W. "Reciprocal Fibonacci Constant". MathWorld.
^ ^a ^b Weisstein, Eric W. "Feigenbaum Constant". MathWorld.
^ Weisstein, Eric W. "Chaitin's Constant". MathWorld.
^ Weisstein, Eric W. "Robbins Constant". MathWorld.
^ Weisstein, Eric W. "Weierstrass Constant". MathWorld.
^ Weisstein, Eric W. "Fransen-Robinson Constant". MathWorld.
^ Weisstein, Eric W. "du Bois-Reymond Constants". MathWorld.
^ Weisstein, Eric W. "Conway's Constant". MathWorld.
^ Weisstein, Eric W. "Hafner-Sarnak-McCurley Constant". MathWorld.
^ Weisstein, Eric W. "Backhouse's Constant". MathWorld.
^ Weisstein, Eric W. "Random Fibonacci Sequence". MathWorld.
^ Weisstein, Eric W. "Komornik-Loreti Constant". MathWorld.
^ Weisstein, Eric W. "Heath-Brown-Moroz Constant". MathWorld.
^ Weisstein, Eric W. "MRB Constant". MathWorld.
^ ^a ^b Weisstein, Eric W. "Somos's Quadratic Recurrence Constant". MathWorld.
^ Weisstein, Eric W. "Foias Constant". MathWorld.
^ Weisstein, Eric W. "Logarithmic Capacity". MathWorld.
^ Weisstein, Eric W. "Taniguchis Constant". MathWorld.
^ Weisstein, Eric W. "Golomb-Dickman Constant Continued Fraction". MathWorld.
^ Weisstein, Eric W. "Catalan's Constant Continued Fraction". MathWorld.
^ Weisstein, Eric W. "Copeland-Erdős Constant Continued Fraction". MathWorld.
^ "Hermite Constants".
^ Weisstein, Eric W. "Relatively Prime". MathWorld.
^ "Favard Constants".

사이트 OEIS.org

사이트 OEIS 위키

^ MRB 상수

서지학

Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 2013-06-05. 카트리오나와 데이비드 리슈카의 영어 번역.
Jensen, Johan Ludwig William Valdemar (1895), "Note numéro 245. Deuxième réponse. Remarques relatives aux réponses du MM. Franel et Kluyver", L'Intermédiaire des Mathématiciens, II: 346–347
Cuyt, Annie A.M.; Petersen, Vigdis; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008). "Mathematical constants". Handbook of Continued Fractions for Special Functions. Dordrecht, Netherlands: Springer Science + Business Media. ISBN 9781402069499.
Borwein, Jonathan; van der Poorten, Alf; Shallit, Jeffrey; Zudilin, Wadim (2014). Neverending Fractions: An Introduction to Continued Fractions. Australian Mathematical Society Lecture Series. Vol. 23. Cambridge, United Kingdom: Cambridge University Press. ISBN 9780521186490. ISSN 0950-2815.

추가열람

Wolfram, Stephen. "4: Systems Based on Numbers". Section 5: Mathematical Constants — Continued fractions. {{cite book}}: work=무시됨(도움말)

외부 링크

[32] $i$ 와 $-i$ 둘 다 이 방정식의 근이지만, 두 근 모두 대수적으로 동치이기 때문에 진정으로 "양의"이거나 다른 근보다 더 기본적이지 않습니다. $i$ 와 $-i$ 의 부호의 구별은 어떤 면에서는 임의적이지만 유용한 표기법 장치입니다.자세한 내용은 상상 단위를 참조하십시오.

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[65] Howard Curtis (2014). Orbital Mechanics for Engineering Students. Elsevier. p. 159. ISBN 978-0-08-097747-8.

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[150] Rees, DG (1987), Foundations of Statistics, CRC Press, p. 246, ISBN 0-412-28560-6, Why 95% confidence? Why not some other confidence level? The use of 95% is partly convention, but levels such as 90%, 98% and sometimes 99.9% are also used.

[151] "Engineering Statistics Handbook: Confidence Limits for the Mean". National Institute of Standards and Technology. Archived from the original on 5 February 2008. Retrieved 4 February 2008. Although the choice of confidence coefficient is somewhat arbitrary, in practice 90%, 95%, and 99% intervals are often used, with 95% being the most commonly used.

[152] Olson, Eric T; Olson, Tammy Perry (2000), Real-Life Math: Statistics, Walch Publishing, p. 66, ISBN 0-8251-3863-9, While other stricter, or looser, limits may be chosen, the 95 percent interval is very often preferred by statisticians.

[153] Swift, MB (2009). "Comparison of Confidence Intervals for a Poisson Mean - Further Considerations". Communications in Statistics - Theory and Methods. 38 (5): 748–759. doi:10.1080/03610920802255856. S2CID 120748700. In modern applied practice, almost all confidence intervals are stated at the 95% level.

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[198] Lowe, I. J. (1959-04-01). "Free Induction Decays of Rotating Solids". Physical Review Letters. 2 (7): 285–287. Bibcode:1959PhRvL...2..285L. doi:10.1103/PhysRevLett.2.285. ISSN 0031-9007.

[199] Paulo Ribenboim (2000). My Numbers, My Friends: Popular Lectures on Number Theory. Springer. p. 66. ISBN 978-0-387-98911-2.

[202] Michel A. Théra (2002). Constructive, Experimental, and Nonlinear Analysis. CMS-AMS. p. 77. ISBN 978-0-8218-2167-1.

[205] Steven Finch (2007). Continued Fraction Transformation (PDF). Harvard University. p. 7. Archived from the original (PDF) on 2016-04-19. Retrieved 2015-02-28.

[209] Robin Whitty. Lieb's Square Ice Theorem (PDF).

[212] Ivan Niven. Averages of exponents in factoring integers (PDF).

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[225] Kathleen T. Alligood (1996). Chaos: An Introduction to Dynamical Systems. Springer. ISBN 978-0-387-94677-1.

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[238] Dusko Letic; Nenad Cakic; Branko Davidovic; Ivana Berkovic. Orthogonal and diagonal dimension fluxes of hyperspherical function (PDF). Springer.

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[2] Weisstein, Eric W. "Pi Formulas". MathWorld.

[8] Weisstein, Eric W. "Pythagoras's Constant". MathWorld.

[12] Weisstein, Eric W. "Theodorus's Constant". MathWorld.

[17] Weisstein, Eric W. "Golden Ratio". MathWorld.

[20] Weisstein, Eric W. "Silver Ratio". MathWorld.

[23] Weisstein, Eric W. "Delian Constant". MathWorld.

[35] Weisstein, Eric W. "Self-Avoiding Walk Connective Constant". MathWorld.

[38] Weisstein, Eric W. "Polygon Inscribing". MathWorld.

[40] Weisstein, Eric W. "Wallis's Constant". MathWorld.

[43] Weisstein, Eric W. "e". MathWorld.

[47] Weisstein, Eric W. "Natural Logarithm of 2". MathWorld.

[52] Weisstein, Eric W. "Lemniscate Constant". MathWorld.

[54] Weisstein, Eric W. "Euler–Mascheroni Constant". MathWorld.

[57] Weisstein, Eric W. "Erdos-Borwein Constant". MathWorld.

[60] Weisstein, Eric W. "Omega Constant". MathWorld.

[63] Weisstein, Eric W. "Apéry's Constant". MathWorld.

[66] Weisstein, Eric W. "Laplace Limit". MathWorld.

[70] Weisstein, Eric W. "Soldner's Constant". MathWorld.

[:4-73] Weisstein, Eric W. "Gauss's Constant". MathWorld.

[77] Weisstein, Eric W. "Hermite Constants". MathWorld.

[80] Weisstein, Eric W. "Liouville's Constant". MathWorld.

[82] Weisstein, Eric W. "Continued Fraction Constants". MathWorld.

[86] Weisstein, Eric W. "Ramanujan Constant". MathWorld.

[88] Weisstein, Eric W. "Glaisher-Kinkelin Constant". MathWorld.

[93] Weisstein, Eric W. "Catalan's Constant". MathWorld.

[:1-96] Weisstein, Eric W. "Dottie Number". MathWorld.

[99] Weisstein, Eric W. "Mertens Constant". MathWorld.

[102] Weisstein, Eric W. "Universal Parabolic Constant". MathWorld.

[106] Weisstein, Eric W. "Cahen's Constant". MathWorld.

[109] Weisstein, Eric W. "Gelfonds Constant". MathWorld.

[113] Weisstein, Eric W. "Gelfond-Schneider Constant". MathWorld.

[116] Weisstein, Eric W. "Favard Constants". MathWorld.

[119] Weisstein, Eric W. "Golden Angle". MathWorld.

[122] Weisstein, Eric W. "Sierpinski Constant". MathWorld.

[125] Weisstein, Eric W. "Landau-Ramanujan Constant". MathWorld.

[128] Weisstein, Eric W. "Nielsen-Ramanujan Constants". MathWorld.

[131] Weisstein, Eric W. "Gieseking's Constant". MathWorld.

[134] Weisstein, Eric W. "Bernstein's Constant". MathWorld.

[137] Weisstein, Eric W. "Tribonacci Constant". MathWorld.

[Brun's_Constant-140] Weisstein, Eric W. "Brun's Constant". MathWorld.

[142] Weisstein, Eric W. "Twin Primes Constant". MathWorld.

[145] Weisstein, Eric W. "Plastic Constant". MathWorld.

[148] Weisstein, Eric W. "Bloch Constant". MathWorld.

[154] Weisstein, Eric W. "Confidence Interval". MathWorld.

[156] Weisstein, Eric W. "Landau Constant". MathWorld.

[159] Weisstein, Eric W. "Thue-Morse Constant". MathWorld.

[162] Weisstein, Eric W. "Golomb-Dickman Constant". MathWorld.

[lebesgue-165] Weisstein, Eric W. "Lebesgue Constants". MathWorld.

[168] Weisstein, Eric W. "Feller-Tornier Constant". MathWorld.

[171] Weisstein, Eric W. "Champernowne Constant". MathWorld.

[174] Weisstein, Eric W. "Salem Constants". MathWorld.

[177] Weisstein, Eric W. "Khinchin's Constant". MathWorld.

[180] Weisstein, Eric W. "Levy Constant". MathWorld.

[183] Weisstein, Eric W. "Levy Constant". MathWorld.

[186] Weisstein, Eric W. "Copeland-Erdos Constant". MathWorld.

[189] Weisstein, Eric W. "Mills Constant". MathWorld.

[192] Weisstein, Eric W. "Gompertz Constant". MathWorld.

[200] Weisstein, Eric W. "Artin's Constant". MathWorld.

[203] Weisstein, Eric W. "Porter's Constant". MathWorld.

[206] Weisstein, Eric W. "Lochs' Constant". MathWorld.

[210] Weisstein, Eric W. "Liebs Square Ice Constant". MathWorld.

[213] Weisstein, Eric W. "Niven's Constant". MathWorld.

[216] Weisstein, Eric W. "Stephen's Constant". MathWorld.

[Paper_Folding_Constant-220] Weisstein, Eric W. "Paper Folding Constant". MathWorld.

[223] Weisstein, Eric W. "Reciprocal Fibonacci Constant". MathWorld.

[Feigenbaum_Constant-226] Weisstein, Eric W. "Feigenbaum Constant". MathWorld.

[229] Weisstein, Eric W. "Chaitin's Constant". MathWorld.

[232] Weisstein, Eric W. "Robbins Constant". MathWorld.

[235] Weisstein, Eric W. "Weierstrass Constant". MathWorld.

[239] Weisstein, Eric W. "Fransen-Robinson Constant". MathWorld.

[244] Weisstein, Eric W. "du Bois-Reymond Constants". MathWorld.

[248] Weisstein, Eric W. "Conway's Constant". MathWorld.

[251] Weisstein, Eric W. "Hafner-Sarnak-McCurley Constant". MathWorld.

[254] Weisstein, Eric W. "Backhouse's Constant". MathWorld.

[257] Weisstein, Eric W. "Random Fibonacci Sequence". MathWorld.

[260] Weisstein, Eric W. "Komornik-Loreti Constant". MathWorld.

[263] Weisstein, Eric W. "Heath-Brown-Moroz Constant". MathWorld.

[268] Weisstein, Eric W. "MRB Constant". MathWorld.

[:2-274] Weisstein, Eric W. "Somos's Quadratic Recurrence Constant". MathWorld.

[Foias-277] Weisstein, Eric W. "Foias Constant". MathWorld.

[281] Weisstein, Eric W. "Logarithmic Capacity". MathWorld.

[283] Weisstein, Eric W. "Taniguchis Constant". MathWorld.

[286] Weisstein, Eric W. "Golomb-Dickman Constant Continued Fraction". MathWorld.

[292] Weisstein, Eric W. "Catalan's Constant Continued Fraction". MathWorld.

[296] Weisstein, Eric W. "Copeland-Erdős Constant Continued Fraction". MathWorld.

[308] "Hermite Constants".

[:3-310] Weisstein, Eric W. "Relatively Prime". MathWorld.

[311] "Favard Constants".

[3] OEIS: A000796

[6] OEIS: A019692

[9] OEIS: A002193

[13] OEIS: A002194

[15] OEIS: A002163

[18] OEIS: A001622

[21] OEIS: A014176

[24] OEIS: A002580

[26] OEIS: A002581

[28] OEIS: A010774

[30] OEIS: A092526

[connective-36] OEIS: A179260

[kepler-39] OEIS: A085365

[41] OEIS: A007493

[44] OEIS: A001113

[48] OEIS: A002162

[53] OEIS: A062539

[55] OEIS: A001620

[58] OEIS: A065442

[61] OEIS: A030178

[apery-64] OEIS: A002117

[67] OEIS: A033259

[solder-71] OEIS: A070769

[74] OEIS: A014549

[78] OEIS: A246724

[81] OEIS: A012245

[83] OEIS: A052119

[87] OEIS: A060295

[glaisher-89] OEIS: A074962

[94] OEIS: A006752

[97] OEIS: A003957

[100] OEIS: A077761

[103] OEIS: A103710

[107] OEIS: A118227

[110] OEIS: A039661

[schneider-114] OEIS: A007507

[117] OEIS: A111003

[120] OEIS: A131988

[123] OEIS: A062089

[landau-126] OEIS: A064533

[129] OEIS: A072691

[132] OEIS: A143298

[135] OEIS: A073001

[138] OEIS: A058265

[:0-141] OEIS: A065421

[143] OEIS: A005597

[plastic-146] OEIS:A060006

[bloch-149] OEIS: A085508

[155] OEIS: A220510

[157] OEIS: A081760

[prouhet-160] OEIS: A014571

[163] OEIS: A084945

[166] OEIS: A243277

[169] OEIS: A065493

[172] OEIS: A033307

[lehmer-175] OEIS: A073011

[178] OEIS: A002210

[181] OEIS: A100199

[184] OEIS: A086702

[copeland-187] OEIS: A033308

[190] OEIS: A051021

[:1-193] OEIS: A073003

[194] OEIS: A163973

[195] OEIS: A163973

[197] OEIS: A195696

[artin-201] OEIS: A005596

[porter-204] OEIS: A086237

[207] OEIS: A086819

[devicci-208] OEIS: A243309

[211] OEIS: A118273

[214] OEIS: A033150

[stephens-217] OEIS: A065478

[paperfolding-221] OEIS: A143347

[:2-224] OEIS: A079586

[227] OEIS: A006890

[230] OEIS: A100264

[robbins-233] OEIS: A073012

[236] OEIS: A094692

[240] OEIS: A058655

[242] OEIS: A006891

[debois-245] OEIS: A062546

[246] OEIS: A074738

[249] OEIS: A014715

[hafner-252] OEIS: A085849

[255] OEIS: A072508

[258] OEIS: A078416

[261] OEIS: A055060

[heath-264] OEIS: A118228

[270] OEIS: A037077

[prime-272] OEIS: A051006

[275] OEIS: A112302

[278] OEIS: A085848

[log_capacity-282] OEIS: A249205

[284] OEIS: A175639

[285] OEIS: A225336

[287] OEIS: A006280

[289] OEIS: A002852

[291] OEIS: A014538

[293] OEIS: A014572

[295] OEIS: A030168

[297] OEIS: A030167

[303] OEIS: A003417

[306] OEIS: A002211

[307] OEIS: A001203

[269] MRB 상수

[1]

[Mw 1]

[OEIS 1]

[3]

[OEIS 2]

[4]

[Mw 2]

[OEIS 3]

[5]

[6]

[Mw 3]

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[9]

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[11]

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[12]

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[13]

[OEIS 11]

[14]

[15]

[16]

[Mw 7]

[OEIS 12]

[17]

[Mw 8]

[OEIS 13]

[Mw 9]

[OEIS 14]

[18]

[Mw 10]

[OEIS 15]

[19]

[20]

[Mw 11]

[OEIS 16]

[21]

[22]

[23]

[Mw 12]

[OEIS 17]

[Mw 13]

[OEIS 18]

[24]

[Mw 14]

[OEIS 19]

[25]

[Mw 15]

[OEIS 20]

[26]

[Mw 16]

[OEIS 21]

[27]

[Mw 17]

[OEIS 22]

[28]

[29]

[Mw 18]

[OEIS 23]

[30]

[Mw 19]

[OEIS 24]

[31]

[32]

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[OEIS 25]

[33]

[Mw 21]

[OEIS 26]

[Mw 22]

[OEIS 27]

[34]

[35]

[Mw 23]

[OEIS 28]

[Mw 24]

[OEIS 29]

[36]

[37]

[38]

[Mw 25]

[OEIS 30]

[39]

[Mw 26]

[OEIS 31]

[40]

[Mw 27]

[OEIS 32]

[41]

[Mw 28]

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