List of mathematical constants

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems.^[1]^[2] For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery.

Explanations of the symbols in the right hand column can be found by clicking on them.

Antiquity[]

Name	Symbol	Decimal expansion	Formula	Year	Set
One	1	1	None^{[nb 1]}	Prehistory	$\mathbb {N}$
Two	2	2	$1+1$	Prehistory	$\mathbb {N}$
One half	1/2	0.5	$1/2$	Prehistory	$\mathbb {Q}$
Pi	$\pi$	3.14159 26535 89793 23846 ^{[Mw 1]}^{[OEIS 1]}	Ratio of a circle's circumference to its diameter.	1900 to 1600 BCE ^[3]	$\mathbb {T}$
Square root of 2, Pythagoras constant.^[4]	${\sqrt {2}}$	1.41421 35623 73095 04880 ^{[Mw 2]}^{[OEIS 2]}	Positive root of $x^{2}=2$	1800 to 1600 BCE^[5]	$\mathbb {A}$
Square root of 3, Theodorus' constant^[6]	${\sqrt {3}}$	1.73205 08075 68877 29352 ^{[Mw 3]}^{[OEIS 3]}	Positive root of $x^{2}=3$	465 to 398 BCE	$\mathbb {A}$
Square root of 5^[7]	${\sqrt {5}}$	2.23606 79774 99789 69640^{[OEIS 4]}	Positive root of $x^{2}=5$		$\mathbb {A}$
Phi, Golden ratio^[1]^[8]	${\varphi }$	1.61803 39887 49894 84820 ^{[Mw 4]}^{[OEIS 5]}	Positive root of $x^{2}-x-1=0$	~300 BCE	$\mathbb {A}$
Zero	0	0	The additive identity: $x+0=x$	300-100 century BCE^[9]	$\mathbb {Z}$
Negative one	−1	−1	$1-2$	300-200 BCE	$\mathbb {Z}$
Cube root of 2 (Delian Constant)	${\sqrt[{3}]{2}}$	1.25992 10498 94873 16476 ^{[Mw 5]}^{[OEIS 6]}	Real root of $x^{3}=2$	46-120 CE^[10]	$\mathbb {A}$
Cube root of 3	${\sqrt[{3}]{3}}$	1.44224 95703 07408 38232^{[OEIS 7]}	Real root of $x^{3}=3$		$\mathbb {A}$

Medieval and Early Modern[]

Name	Symbol	Decimal expansion	Formula	Year	Set
Imaginary unit^[1]^[11]	${i}$	$0 + 1 i$	Either of the two roots of $x^{2}=-1$ ^{[nb 2]}	1501 to 1576	$\mathbb {C}$
Wallis Constant	$W$	2.09455 14815 42326 59148 ^{[Mw 6]}^{[OEIS 8]}	${\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}$	1616 to 1703	$\mathbb {A}$
Euler's number^[1]^[12]	${e}$	2.71828 18284 59045 23536 ^{[Mw 7]}^{[OEIS 9]}	$\lim _{n\to \infty }\!\left(\!1\!+\!{\frac {1}{n}}\right)^{n}$ ^{[nb 3]}	1618^[13]	$\mathbb {T}$
Natural logarithm of 2^[14]	$\ln 2$	0.69314 71805 59945 30941 ^{[Mw 8]}^{[OEIS 10]}	$\sum _{n=1}^{\infty }{\frac {1}{n2^{n}}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+\cdots$	1619,^[15] 1668^[16]	$\mathbb {T}$
Sophomore's dream₁ J.Bernoulli^[17]	${I}_{1}$	0.78343 05107 12134 40705 ^{[OEIS 11]}	$\int _{0}^{1}\!x^{x}\,dx=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}={\frac {1}{1^{1}}}-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-\cdots$	1697
Sophomore's dream₂ J.Bernoulli^[18]	${I}_{2}$	1.29128 59970 62663 54040 ^{[Mw 9]}^{[OEIS 12]}	$\int _{0}^{1}\!{\frac {dx}{x^{x}}}=\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}={\frac {1}{1^{1}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+\cdots$	1697
Lemniscate constant^[19]	${\varpi }$	2.62205 75542 92119 81046 ^{[Mw 10]}^{[OEIS 13]}	$\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {1}{4}}\right)^{2}}=4{\sqrt {\tfrac {2}{\pi }}}\left({\tfrac {1}{4}}!\right)^{2}$	1718 to 1798	$\mathbb {T}$
Euler–Mascheroni constant^[20]	${\gamma }$	0.57721 56649 01532 86060 ^{[Mw 11]}^{[OEIS 14]}	${\begin{aligned}&\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}=\sum _{n=1}^{\infty }\left({\frac {1}{n}}-\ln \left(1+{\frac {1}{n}}\right)\right)\\&=\int _{0}^{1}-\ln \left(\ln {\frac {1}{x}}\right)\,dx=-\Gamma '(1)=-\Psi (1)\end{aligned}}$	1735	$\mathbb {R} \setminus \mathbb {Q}$ ?
Analog of Euler–Mascheroni constant	${\gamma }$	0.42816 57248 71235 07519	$\lim _{n\to \infty }\!\left(\sum _{k=2}^{n}{\frac {1}{k\ln(k)}}-\ln \left(\ln(n)\right)+\ln \left(\ln(2)\right)\!\right)$	1735 to 1745	$\mathbb {T}$ ?
Erdős–Borwein constant^[21]	${E}_{\,B}$	1.60669 51524 15291 76378 ^{[Mw 12]}^{[OEIS 15]}	$\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {1}{2^{mn}}}=\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!\cdots$	1749^[22]	$\mathbb {R} \setminus \mathbb {Q}$
Laplace limit^[23]	${\lambda }$	0.66274 34193 49181 58097 ^{[Mw 13]}^{[OEIS 16]}	${\frac {x\;e^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$	~1782	$\mathbb {T}$ ?
Gauss's constant^[24]	${G}$	0.83462 68416 74073 18628 ^{[Mw 14]}^{[OEIS 17]}	${\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,\left({\tfrac {1}{4}}!\right)^{2}}{\pi ^{3}{2}}}={\frac {2}{\pi }}\int _{0}^{1}{\frac {dx}{\sqrt {1-x^{4}}}}$ where agm is the arithmetic–geometric mean	1799^[25]	$\mathbb {T}$

19th century[]

Name	Symbol	Decimal expansion	Formula	Year	Set
Ramanujan–Soldner constant^[26]^[27]	${\mu }$	1.45136 92348 83381 05028 ^{[Mw 15]}^{[OEIS 18]}	$\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$ ; root of the logarithmic integral function.	1812^{[Mw 16]}
Hermite constant^[28]	$\gamma _{_{2}}$	1.15470 05383 79251 52901 ^{[Mw 17]}	${\frac {2}{\sqrt {3}}}={\frac {1}{\cos \,({\frac {\pi }{6}})}}$	1822 to 1901	$\mathbb {A}$
Liouville number^[29]	${\text{£}}_{Li}$	0.11000 10000 00000 00000 0001 ^{[Mw 18]}^{[OEIS 19]}	$\sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots$	Before 1844	$\mathbb {T}$
Split-complex unity	$j$	0+1j	Either of the two roots of $x^{2}=1$ , which are neither $1$ or $-1$	1848	Split-complex numbers, Tessarines
Hermite–Ramanujan constant^[30]	${R}$	262 53741 26407 68743 .99999 99999 99250 073 ^{[Mw 19]}^{[OEIS 20]}	$e^{\pi {\sqrt {163}}}$	1859	$\mathbb {T}$
Catalan's constant^[31]^[32]^[33]	${C}$	0.91596 55941 77219 01505 ^{[Mw 20]}^{[OEIS 21]}	$\int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {dx\,dy}{1{+}x^{2}y^{2}}}=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }$	1864	$\mathbb {T}$ ?
Dottie number^[34]	$d$	0.73908 51332 15160 64165 ^{[Mw 21]}^{[OEIS 22]}	$\lim _{x\to \infty }\cos ^{[x]}(c)=\lim _{x\to \infty }\underbrace {\cos(\cos(\cos(\cdots (\cos(c)))))} _{x}$	1865^{[Mw 21]}	$\mathbb {T}$
Meissel–Mertens constant^[35]	${M}$	0.26149 72128 47642 78375 ^{[Mw 22]}^{[OEIS 23]}	$\lim _{n\to \infty }\!\!\left(\sum _{p\leq n}{\frac {1}{p}}\!-\ln(\ln(n))\!\right)\!\!={\!\gamma \!+\!\!\sum _{p}\!\left(\!\ln \!\left(\!1\!-\!{\frac {1}{p}}\!\right)\!\!+\!{\frac {1}{p}}\!\right)}$ where γ is Euler's constant and p is a prime	1866 & 1873	$\mathbb {T}$ ?
Weierstrass constant ^[36]	$\sigma ({\tfrac {1}{2}})$	0.47494 93799 87920 65033 ^{[Mw 23]}^{[OEIS 24]}	${\frac {e^{{\pi }/{8}}{\sqrt {\pi }}}{4\cdot 2^{3/4}{\left({\frac {1}{4}}!\right)^{2}}}}$	1872 ?
Dual unity	$\varepsilon$	0+1ε		1873	Dual numbers
Hafner–Sarnak–McCurley constant (2) ^[37]	${\frac {1}{\zeta (2)}}$	0.60792 71018 54026 62866 ^{[Mw 24]}^{[OEIS 25]}	${\frac {6}{\pi ^{2}}}=\prod _{n=0}^{\infty }{\!\left(\!1-{\frac {1}{{p_{n}}^{2}}}\!\right)}\!=\!\textstyle \left(1\!-\!{\frac {1}{2^{2}}}\right)\!\left(1\!-\!{\frac {1}{3^{2}}}\right)\!\left(1\!-\!{\frac {1}{5^{2}}}\right)\cdots$ where p_n is a prime	1883^{[Mw 24]}	$\mathbb {T}$
Cahen's constant^[38]	$\xi _{2}$	0.64341 05462 88338 02618 ^{[Mw 25]}^{[OEIS 26]}	$\sum _{k=1}^{\infty }{\frac {(-1)^{k}}{s_{k}-1}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{6}}-{\frac {1}{42}}+{\frac {1}{1806}}{\,\pm \cdots }$ Where s_k is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ... Defined as: $S_{0}=\,2,\,\,S_{k}=\,1+\prod _{n=0}^{k-1}S_{n}{\text{ for }}k>0$	1891	$\mathbb {T}$
Universal parabolic constant^[39]	${P}_{\,2}$	2.29558 71493 92638 07403 ^{[Mw 26]}^{[OEIS 27]}	$\ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arsinh} (1)+{\sqrt {2}}$	Before 1891^[40]	$\mathbb {T}$
Apéry's constant^[41]	$\zeta (3)$	1.20205 69031 59594 28539 ^{[Mw 27]}^{[OEIS 28]}	$\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots =$ ${\frac {1}{2}}\sum _{n=1}^{\infty }{\frac {H_{n}}{n^{2}}}={\frac {1}{2}}\sum _{i=1}^{\infty }\sum _{j=1}^{\infty }{\frac {1}{ij(i{+}j)}}=\!\!\int _{0}^{1}\!\!\int _{0}^{1}\!\!\int _{0}^{1}{\frac {dx\,dy\,dz}{1-xyz}}$	1895^[42]	$\mathbb {R} \setminus \mathbb {Q}$ $\mathbb {T}$ ?
Gelfond's constant^[43]	${e}^{\pi }$	23.14069 26327 79269 0057 ^{[Mw 28]}^{[OEIS 29]}	$(-1)^{-i}=i^{-2i}=\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}=1+{\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2}}+{\frac {\pi ^{3}}{6}}+\cdots$	1900^[44]	$\mathbb {T}$

1900–1949[]

Name	Symbol	Decimal expansion	Formula	Year	Set
Favard constant^[45]	${\tfrac {3}{4}}\zeta (2)$	1.23370 05501 36169 82735 ^{[Mw 29]}^{[OEIS 30]}	${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots$	1902 to 1965	$\mathbb {T}$
Golden angle^[46]	${b}$	2.39996 32297 28653 32223 ^{[Mw 30]}^{[OEIS 31]}	$(4-2\,\Phi )\,\pi =(3-{\sqrt {5}})\,\pi$ = 137.5077640500378546 ...°	1907	$\mathbb {T}$
Sierpiński's constant^[47]	${K}$	2.58498 17595 79253 21706 ^{[Mw 31]}^{[OEIS 32]}	${\begin{aligned}&\pi \left(2\gamma +\ln {\frac {4\pi ^{3}}{\Gamma ({\tfrac {1}{4}})^{4}}}\right)=\pi (2\gamma +4\ln \Gamma ({\tfrac {3}{4}})-\ln \pi )\\&=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)\end{aligned}}$	1907
Nielsen–Ramanujan constant ^[48]	${\frac {{\zeta }(2)}{2}}$	0.82246 70334 24113 21823 ^{[Mw 32]}^{[OEIS 33]}	${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}{-}\cdots$	1909	$\mathbb {T}$
Area of the Mandelbrot fractal^[49]	$\gamma$	1.5065918849 ± 0.0000000028 ^{[Mw 33]}^{[OEIS 34]}		1912
Gieseking constant^[50]	${\pi \ln \beta }$	1.01494 16064 09653 62502 ^{[Mw 34]}^{[OEIS 35]}	${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$ .	1912
Bernstein's constant^[51]	${\beta }$	0.28016 94990 23869 13303 ^{[Mw 35]}^{[OEIS 36]}	$\approx {\frac {1}{2{\sqrt {\pi }}}}$	1913
Twin Primes Constant	${C}_{2}$	0.66016 18158 46869 57392 ^{[Mw 36]}^{[OEIS 37]}	$\prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}$	1922
Plastic number^[52]	${\rho }$	1.32471 79572 44746 02596 ^{[Mw 37]}^{[OEIS 38]}	${\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {\sqrt {69}}{18}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {\sqrt {69}}{18}}}}$	1929	$\mathbb {A}$
Bloch–Landau constant^[53]	${L}$	0.54325 89653 42976 70695 ^{[Mw 38]}^{[OEIS 39]}	${\frac {\Gamma ({\tfrac {1}{3}})\;\Gamma ({\tfrac {5}{6}})}{\Gamma ({\tfrac {1}{6}})}}={\frac {(-{\tfrac {2}{3}})!\;(-1+{\tfrac {5}{6}})!}{(-1+{\tfrac {1}{6}})!}}$	1929
Golomb–Dickman constant^[54]	${\lambda }$	0.62432 99885 43550 87099 ^{[Mw 39]}^{[OEIS 40]}	$\int _{0}^{\infty }{\underset {{\text{Para }}x>2}{{\frac {f(x)}{x^{2}}}\,dx}}=\int _{0}^{1}e^{\operatorname {Li} (n)}dn$ where Li is the logarithmic integral	1930 & 1964
Feller–Tornier constant^[55]	${{\mathcal {C}}_{_{FT}}}$	0.66131 70494 69622 33528 ^{[Mw 40]}^{[OEIS 41]}	${\underset {p_{n}:\,{prime}}{{\frac {1}{2}}\prod _{n=1}^{\infty }\left(1-{\frac {2}{p_{n}^{2}}}\right){+}{\frac {1}{2}}}}={\frac {3}{\pi ^{2}}}\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}^{2}-1}}\right){+}{\frac {1}{2}}$ where p_n is a prime	1932	$\mathbb {T}$ ?
Base 10 Champernowne constant^[56]	$C_{10}$	0.12345 67891 01112 13141 ^{[Mw 41]}^{[OEIS 42]}	$\sum _{n=1}^{\infty }\;\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{j=0}^{n-1}10^{j}(n-j-1)}}}$	1933	$\mathbb {T}$
Gelfond–Schneider constant^[57]	$G_{\,GS}$	2.66514 41426 90225 18865 ^{[Mw 42]}^{[OEIS 43]}	$2^{\sqrt {2}}$	1934	$\mathbb {T}$
Khinchin's constant^[58]	$K_{\,0}$	2.68545 20010 65306 44530 ^{[Mw 43]}^{[OEIS 44]}	$\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	1934	$\mathbb {T}$ ?
Khinchin–Lévy constant^[59]	${\beta }$	1.18656 91104 15625 45282 ^{[Mw 44]}^{[OEIS 45]}	${\frac {\pi ^{2}}{12\,\ln 2}}$	1935
Khinchin-Lévy constant^[60]	$e^{\beta }$	3.27582 29187 21811 15978 ^{[Mw 45]}^{[OEIS 46]}	$e^{\pi ^{2}/(12\ln 2)}$	1936
Mills' constant^[61]	${\theta }$	1.30637 78838 63080 69046 ^{[Mw 46]}^{[OEIS 47]}	$\lfloor \theta ^{3^{n}}\rfloor$ is prime	1947
Euler–Gompertz constant^[62]	${G}$	0.59634 73623 23194 07434 ^{[Mw 47]}^{[OEIS 48]}	$\int _{0}^{\infty }\!\!{\frac {e^{-n}}{1{+}n}}\,dn=\!\!\int _{0}^{1}\!\!{\frac {dn}{1{-}\ln n}}={\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {2}{1+{\tfrac {2}{1+{\tfrac {3}{1+3{/\cdots }}}}}}}}}}}}}$	Before 1948^{[OEIS 48]}

1950–1999[]

Name	Symbol	Decimal expansion	Formula	Year	Set
Van der Pauw constant	${\frac {\pi }{\ln 2}}$	4.53236 01418 27193 80962^{[OEIS 49]}	${\frac {\sum \limits _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+{\frac {4}{9}}-\cdots }{{\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots }}$	Before 1958^{[OEIS 50]}
Magic angle^[63]	${\theta _{m}}$	0.95531 66181 245092 78163^{[OEIS 51]}	$\arctan {\sqrt {2}}=\arccos {\tfrac {1}{\sqrt {3}}}\approx \textstyle {54.7356}^{\circ }$	Before 1959^[64]^[63]	$\mathbb {T}$
Lochs constant^[65]	${{\text{£}}_{_{Lo}}}$	0.97027 01143 92033 92574 ^{[Mw 48]}^{[OEIS 52]}	${\frac {6\ln 2\ln 10}{\pi ^{2}}}$	1964
Lieb's square ice constant^[66]	${W}_{2D}$	1.53960 07178 39002 03869 ^{[Mw 49]}^{[OEIS 53]}	$\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}$	1967	$\mathbb {A}$
Niven's constant^[67]	${C}$	1.70521 11401 05367 76428 ^{[Mw 50]}^{[OEIS 54]}	$1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)$	1969
Baker constant^[68]	$\beta _{3}$	0.83564 88482 64721 05333^{[OEIS 55]}	$\int _{0}^{1}{\frac {\mathrm {d} t}{1+t^{3}}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{3n+1}}={\frac {1}{3}}\left(\ln 2+{\frac {\pi }{\sqrt {3}}}\right)$	Before 1969^[68]	$\mathbb {T}$
Porter's constant^[69]	${C}$	1.46707 80794 33975 47289 ^{[Mw 51]}^{[OEIS 56]}	${\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}$ where γ (= 0.5772156649...) is the Euler–Mascheroni Constant $\scriptstyle \zeta '(2)\,{\text{= Derivative of }}\zeta (2)=-\sum \limits _{n=2}^{\infty }{\frac {\ln n}{n^{2}}}=-0.9375482543\ldots$	1974
Feigenbaum constant δ ^[70]	${\delta }$	4.66920 16091 02990 67185 ^{[Mw 52]}^{[OEIS 57]}	$\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3.8284;\,3.8495)$ $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {\text{or}}\quad x_{n+1}=\,a\sin(x_{n})$	1975
Chaitin's constants ^[71]	$\Omega$	In general they are uncomputable numbers. But one such number is 0.00787 49969 97812 3844 ^{[Mw 53]}^{[OEIS 58]}	$\sum _{p\in P}2^{-\|p\|}$ $p$ : Halted program $\| p \|$ : Size in bits of program $p$ $P$ : Domain of all programs that stop. See also: Halting problem	1975	$\mathbb {T}$
Fransén–Robinson constant^[72]	${F}$	2.80777 02420 28519 36522 ^{[Mw 54]}^{[OEIS 59]}	$\int _{0}^{\infty }{\frac {dx}{\Gamma (x)}}=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	1978
Robbins constant^[73]	$\Delta (3)$	0.66170 71822 67176 23515 ^{[Mw 55]}^{[OEIS 60]}	${\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}$	1978	$\mathbb {T}$
Feigenbaum constant α^[74]	$\alpha$	2.50290 78750 95892 82228 ^{[Mw 52]}^{[OEIS 61]}	$\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$	1979	$\mathbb {T}$ ?
Fractal dimension of the Cantor set^[75]	$d_{f}(k)$	0.63092 97535 71457 43709 ^{[Mw 56]}^{[OEIS 62]}	$\lim _{\varepsilon \to 0}{\frac {\log N(\varepsilon )}{\log(1/\varepsilon )}}={\frac {\log 2}{\log 3}}$	Before 1979^{[OEIS 62]}	$\mathbb {T}$
Connective constant^[76]^[77]	${\mu }$	1.84775 90650 22573 51225 ^{[Mw 57]}^{[OEIS 63]}	${\sqrt {2+{\sqrt {2}}}}\;=\lim _{n\rightarrow \infty }c_{n}^{1/n}$ as a root of the polynomial $:\;x^{4}-4x^{2}+2=0$	1982^[78]	$\mathbb {A}$
Lehmer's conjecture constant^[79]	${\sigma _{_{10}}}$	1.17628 08182 59917 50654 ^{[Mw 58]}^{[OEIS 64]}	$x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1$	1983?	$\mathbb {A}$
Chebyshev constant^[80] · ^[81]	$\lambda _{\text{Ch}}$	0.59017 02995 08048 11302 ^{[Mw 59]}^{[OEIS 65]}	${\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}={\frac {4({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}$	Before 1987^{[Mw 59]}
Conway constant^[82]	${\lambda }$	1.30357 72690 34296 39125 ^{[Mw 60]}^{[OEIS 66]}	${\begin{smallmatrix}x^{71}\quad \ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad \ -7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}\quad \ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}$	1987	$\mathbb {A}$
Prévost constant, Reciprocal Fibonacci constant^[83]	$\Psi$	3.35988 56662 43177 55317 ^{[Mw 61]}^{[OEIS 67]}	$\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ F_n: Fibonacci series	Before 1988^{[OEIS 67]}	$\mathbb {R} \setminus \mathbb {Q}$
Brun₂ constant = Σ inverse of Twin primes ^[84]	${B}_{\,2}$	1.90216 05831 04 ^{[Mw 62]}^{[OEIS 68]}	$\textstyle {\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+2}})}=({\frac {1}{3}}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}})+\cdots$ where p is a prime such that p + 2 is also a prime	1989^{[OEIS 68]}
Hafner–Sarnak–McCurley constant (1) ^[85]	${\sigma }$	0.35323 63718 54995 98454 ^{[Mw 63]}^{[OEIS 69]}	$\prod _{k=1}^{\infty }\left\{1-\left[1-\prod _{j=1}^{n}\left(1-p_{k}^{-j}\right)\right]^{2}\right\}$ where p_k is a prime	1993
Fractal dimension of the Apollonian packing of circles ^[86]^[87]	$\varepsilon$	1.30568 6729 ≈ by Thomas & Dhar 1.30568 8 ≈ by McMullen ^{[Mw 64]}^{[OEIS 70]}		1994 1998
Backhouse's constant^[88]	${B}$	1.45607 49485 82689 67139 ^{[Mw 65]}^{[OEIS 71]}	$\lim _{k\to \infty }\left\|{\frac {q_{k+1}}{q_{k}}}\right\vert \quad \scriptstyle {\text{where:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty }q_{k}x^{k}$ $P(x)=\sum _{k=1}^{\infty }{\underset {p_{k}{\text{ prime}}}{p_{k}x^{k}}}=1+2x+3x^{2}+5x^{3}+\cdots$	1995
Viswanath constant^[89]	${C}_{Vi}$	1.13198 82487 943 ^{[Mw 66]}^{[OEIS 72]}	$\lim _{n\to \infty }\|a_{n}\|^{\frac {1}{n}}$ where a_n = Fibonacci sequence	1997	$\mathbb {T}$ ?
Time constant ^[90]	${\tau }$	0.63212 05588 28557 67840 ^{[Mw 67]}^{[OEIS 73]}	$\lim _{n\to \infty }1-{\frac {!n}{n!}}=\lim _{n\to \infty }P(n)=\int _{0}^{1}e^{-x}dx=1{-}{\frac {1}{e}}=$ $\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n!}}={\frac {1}{1!}}{-}{\frac {1}{2!}}{+}{\frac {1}{3!}}{-}{\frac {1}{4!}}{+}{\frac {1}{5!}}{-}{\frac {1}{6!}}{+}\cdots$	Before 1997^[90]	$\mathbb {T}$
Komornik–Loreti constant^[91]	${q}$	1.78723 16501 82965 93301 ^{[Mw 68]}^{[OEIS 74]}	$1=\!\sum _{n=1}^{\infty }{\frac {t_{k}}{q^{k}}}\qquad \scriptstyle {\text{Raiz real de}}\displaystyle \prod _{n=0}^{\infty }\!\left(\!1{-}{\frac {1}{q^{2^{n}}}}\!\right)\!{+}{\frac {q{-}2}{q{-}1}}=0$ t_k = Thue–Morse sequence	1998	$\mathbb {T}$
Regular paperfolding sequence^[92]^[93]	${P_{f}}$	0.85073 61882 01867 26036 ^{[Mw 69]}^{[OEIS 75]}	$\sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}$	Before 1998^[93]
Artin constant^[94]	${C}_{Artin}$	0.37395 58136 19202 28805 ^{[Mw 70]}^{[OEIS 76]}	$\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)\quad p_{n}\scriptstyle {\text{ = prime}}$	1999
MRB constant^[95]^[96]^[97]	$C_{{}_{MRB}}$	0.18785 96424 62067 12024 ^{[Mw 71]}^{[Ow 1]}^{[OEIS 77]}	$\sum _{n=1}^{\infty }(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots$	1999
Somos' quadratic recurrence constant^[98]	${\sigma }$	1.66168 79496 33594 12129 ^{[Mw 72]}^{[OEIS 78]}	$\prod _{n=1}^{\infty }n^{{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots$	1999^{[Mw 72]}	$\mathbb {T}$ ?

2000 onwards[]

Name	Symbol	Decimal expansion	Formula	Year	Set
Foias constant _α ^[99]	$F_{\alpha }$	1.18745 23511 26501 05459 ^{[Mw 73]}^{[OEIS 79]}	$x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ for }}n=1,2,3,\ldots$ Foias constant is the unique real number such that if x₁ = α then the sequence diverges to ∞. When x₁ = α, $\,\lim _{n\to \infty }x_{n}{\tfrac {\log n}{n}}=1$	2000
Foias constant _β	$F_{\beta }$	2.29316 62874 11861 03150 ^{[Mw 73]}^{[OEIS 80]}	$x^{x+1}=(x+1)^{x}$	2000
Raabe's formula^[100]	${\zeta '(0)}$	0.91893 85332 04672 74178 ^{[Mw 74]}^{[OEIS 81]}	$\int _{a}^{a+1}\log \Gamma (t)\,dt={\tfrac {1}{2}}\log 2\pi +a\log a-a,\quad a\geq 0$	Before 2011^[100]
Kepler–Bouwkamp constant^[101]	${\rho }$	0.11494 20448 53296 20070 ^{[Mw 75]}^{[OEIS 82]}	$\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...$	Before 2013^[101]
Prouhet–Thue–Morse constant^[102]	$\tau$	0.41245 40336 40107 59778 ^{[Mw 76]}^{[OEIS 83]}	$\sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}$ where ${t_{n}}$ is the Thue–Morse sequence and Where $\tau (x)=\sum _{n=0}^{\infty }(-1)^{t_{n}}\,x^{n}=\prod _{n=0}^{\infty }(1-x^{2^{n}})$	Before 2014^[102]	$\mathbb {T}$
Heath-Brown–Moroz constant^[103]	${C_{_{HBM}}}$	0.00131 76411 54853 17810 ^{[Mw 77]}^{[OEIS 84]}	${\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}}}\right)^{7}\left(1+{\frac {7p_{n}+1}{p_{n}^{2}}}\right)}}$	Before 2002^[103]	$\mathbb {T}$ ?
Lebesgue constant^[104]	${C_{1}}$	0.98943 12738 31146 95174 ^{[Mw 78]}^{[OEIS 85]}	$\lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)$	Before 2002^[104]
2nd du Bois-Reymond constant^[105]	${C_{2}}$	0.19452 80494 65325 11361 ^{[Mw 79]}^{[OEIS 86]}	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left\|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{n}}\right\|\,dt-1$	Before 2003^[105]	$\mathbb {T}$
Stephens constant^[106]	$C_{S}$	0.57595 99688 92945 43964 ^{[Mw 80]}^{[OEIS 87]}	$\prod _{n=1}^{\infty }\left(1-{\frac {p}{p^{3}-1}}\right)$	Before 2005^[106]	$\mathbb {T}$ ?
Taniguchi constant^[106]	$C_{T}$	0.67823 44919 17391 97803 ^{[Mw 81]}^{[OEIS 88]}	$\prod _{n=1}^{\infty }\left(1-{\frac {3}{{p_{n}}^{3}}}+{\frac {2}{{p_{n}}^{4}}}+{\frac {1}{{p_{n}}^{5}}}-{\frac {1}{{p_{n}}^{6}}}\right)$ $\scriptstyle p_{n}=\,{\text{prime}}$	Before 2005^[106]	$\mathbb {T}$ ?
Copeland–Erdős constant^[107]	${{\mathcal {C}}_{CE}}$	0.23571 11317 19232 93137 ^{[Mw 82]}^{[OEIS 89]}	$\sum _{n=1}^{\infty }{\frac {p_{n}}{10^{n+\sum \limits _{k=1}^{n}\lfloor \log _{10}{p_{k}}\rfloor }}}$	Before 2012^[107]	$\mathbb {R} \setminus \mathbb {Q}$
Hausdorff dimension, Sierpinski triangle^[108]	${\log _{2}3}$	1.58496 25007 21156 18145 ^{[Mw 83]}^{[OEIS 90]}	${\frac {\log 3}{\log 2}}={\frac {\sum _{n=0}^{\infty }{\frac {1}{2^{2n+1}(2n+1)}}}{\sum _{n=0}^{\infty }{\frac {1}{3^{2n+1}(2n+1)}}}}={\frac {{\frac {1}{2}}+{\frac {1}{24}}+{\frac {1}{160}}+\cdots }{{\frac {1}{3}}+{\frac {1}{81}}+{\frac {1}{1215}}+\cdots }}$	Before 2002^[108]	$\mathbb {T}$
Landau–Ramanujan constant^[109]	$K$	0.76422 36535 89220 66299 ^{[Mw 84]}^{[OEIS 91]}	${\frac {1}{\sqrt {2}}}\prod _{p\equiv 3\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!\!\!\!\!p:{\text{ prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}}\!\!={\frac {\pi }{4}}\prod _{p\equiv 1\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!p:{\text{ prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}}$	Before 2005^[109]	$\mathbb {T}$ ?
Brun₄ constant = Σ inv.prime quadruplets ^[110]	${B}_{\,4}$	0.87058 83799 75 ^{[Mw 62]}^{[OEIS 92]}	$\textstyle {\sum ({\frac {1}{p}}+{\frac {1}{p+2}}+{\frac {1}{p+6}}+{\frac {1}{p+8}})}\scriptstyle \quad {p,\;p+2,\;p+6,\;p+8:{\text{ prime}}}$ $\textstyle {\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$	Before 2002^[110]
Ramanujan nested radical^[111]	$R_{5}$	2.74723 82749 32304 33305	$\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	Before 2001^[111]	$\mathbb {A}$
Slowly convergent series constant	${a}_{2}$	2.10974 28012 36891 97447 ^{[Mw 85]}^{[OEIS 93]}	$\sum _{n=2}^{\infty }{\frac {1}{n\ln ^{2}(n)}}$	2006	$\mathbb {T}$ ?

Other constants[]

Name	Symbol	Decimal expansion	Formula	Set
DeVicci's tesseract constant	${f_{(3,4)}}$	1.00743 47568 84279 37609^{[Mw 86]}^{[OEIS 94]}	The largest cube that can pass through in an 4D hypercube. Positive root of $4x^{4}{-}28x^{3}{-}7x^{2}{+}16x{+}16=0$	$\mathbb {A}$
Glaisher–Kinkelin constant	${A}$	1.28242 71291 00622 63687^{[Mw 87]}^{[OEIS 95]}	$e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$
Unique local minimum of the function $f(x)=\sum _{n=2}^{\infty }{\frac {1}{n\ln ^{x}(n)}}$	${L}$	$2.4<{L}<2.5$	$\sum _{n=2}^{\infty }{\frac {\ln(\ln(n))}{n\ln ^{L}(n)}}=0$	$\mathbb {T}$ ?

Notes[]

^ 1 can be given as a primitive notion within Peano arithmetic. Alternatively, 0 can be a primitive notion in Peano arithmetic and 1 defined as the successor to 0. This article uses the former definition for pedagogical and chronological simplicity.
^ Both $i$ and $- i$ are roots of this equation, though neither root is truly "positive" nor more fundamental than the other as they are algebraically equivalent. The distinction between signs of $i$ and $- i$ is in some ways arbitrary, but a useful notational device. See imaginary unit for more information.
^ Can also be defined by the infinite series ${\textstyle \sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+\cdots }$

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^ Jump up to: ^a ^b Steven R. Finch (2003). Mathematical Constants. Cambridge University Press. p. 238. ISBN 978-3-540-67695-9.
^ Jump up to: ^a ^b ^c ^d Steven Finch (2005). Class Number Theory (PDF). Harvard University. p. 8. Archived from the original (PDF) on 2016-04-19. Retrieved 2014-04-15.
^ Jump up to: ^a ^b Yann Bugeaud (2012). Distribution Modulo One and Diophantine Approximation. Cambridge University Press. p. 87. ISBN 978-0-521-11169-0.
^ Jump up to: ^a ^b Eric W. Weisstein (2002). CRC Concise Encyclopedia of Mathematics (Second ed.). CRC Press. p. 1356. ISBN 978-1-58488-347-0.
^ Jump up to: ^a ^b Richard E. Crandall; Carl B. Pomerance (2005). Prime Numbers: A Computational Perspective. Springer. p. 80. ISBN 978-0387-25282-7.
^ Jump up to: ^a ^b Pascal Sebah & Xavier Gourdon (2002). Introduction to twin primes and Brun's constant computation (PDF).
^ Jump up to: ^a ^b Bruce C. Berndt; Robert Alexander Rankin (2001). Ramanujan: essays and surveys. American Mathematical Society, London Mathematical Society. p. 219. ISBN 978-0-8218-2624-9.

Site 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. "Delian Constant". MathWorld.
^ Weisstein, Eric W. "Wallis's Constant". MathWorld.
^ Weisstein, Eric W. "e". MathWorld.
^ Weisstein, Eric W. "Natural Logarithm of 2". MathWorld.
^ Weisstein, Eric W. "Sophomore's Dream". MathWorld.
^ Weisstein, Eric W. "Lemniscate Constant". MathWorld.
^ Weisstein, Eric W. "Euler–Mascheroni Constant". MathWorld.
^ Weisstein, Eric W. "Erdos-Borwein Constant". MathWorld.
^ Weisstein, Eric W. "Laplace Limit". MathWorld.
^ Weisstein, Eric W. "Gauss's Constant". MathWorld.
^ Weisstein, Eric W. "Soldner's Constant". MathWorld.
^ Weisstein, Eric W. "Soldner's Constant". MathWorld.
^ Weisstein, Eric W. "Hermite Constants". MathWorld.
^ Weisstein, Eric W. "Liouville's Constant". MathWorld.
^ Weisstein, Eric W. "Ramanujan Constant". MathWorld.
^ Weisstein, Eric W. "Catalan's Constant". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "Dottie Number". MathWorld.
^ Weisstein, Eric W. "Mertens Constant". MathWorld.
^ Weisstein, Eric W. "Weierstrass Constant". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "Relatively Prime". MathWorld.
^ Weisstein, Eric W. "Cahen's Constant". MathWorld.
^ Weisstein, Eric W. "Universal Parabolic Constant". MathWorld.
^ Weisstein, Eric W. "Apéry's Constant". MathWorld.
^ Weisstein, Eric W. "Gelfonds Constant". MathWorld.
^ Weisstein, Eric W. "Favard Constants". MathWorld.
^ Weisstein, Eric W. "Golden Angle". MathWorld.
^ Weisstein, Eric W. "Sierpinski Constant". MathWorld.
^ Weisstein, Eric W. "Nielsen-Ramanujan Constants". MathWorld.
^ Weisstein, Eric W. "Mandelbrot Set". MathWorld.
^ Weisstein, Eric W. "Gieseking's Constant". MathWorld.
^ Weisstein, Eric W. "Bernstein's Constant". MathWorld.
^ Weisstein, Eric W. "Twin Primes Constant". MathWorld.
^ Weisstein, Eric W. "Plastic Constant". MathWorld.
^ Weisstein, Eric W. "Landau Constant". MathWorld.
^ Weisstein, Eric W. "Golomb-Dickman Constant". MathWorld.
^ Weisstein, Eric W. "Feller-Tornier Constant". MathWorld.
^ Weisstein, Eric W. "Champernowne Constant". MathWorld.
^ Weisstein, Eric W. "Gelfond-Schneider Constant". MathWorld.
^ Weisstein, Eric W. "Khinchin's Constant". MathWorld.
^ Weisstein, Eric W. "Levy Constant". MathWorld.
^ Weisstein, Eric W. "Levy Constant". MathWorld.
^ Weisstein, Eric W. "Mills Constant". MathWorld.
^ Weisstein, Eric W. "Gompertz 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. "Porter's Constant". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "Feigenbaum Constant". MathWorld.
^ Weisstein, Eric W. "Chaitin's Constant". MathWorld.
^ Weisstein, Eric W. "Fransen-Robinson Constant". MathWorld.
^ Weisstein, Eric W. "Robbins Constant". MathWorld.
^ Weisstein, Eric W. "Cantor Set". MathWorld.
^ Weisstein, Eric W. "Self-Avoiding Walk Connective Constant". MathWorld.
^ Weisstein, Eric W. "Salem Constants". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "Chebyshev Constants". MathWorld.
^ Weisstein, Eric W. "Conway's Constant". MathWorld.
^ Weisstein, Eric W. "Reciprocal Fibonacci Constant". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "Brun's Constant". MathWorld.
^ Weisstein, Eric W. "Hafner-Sarnak-McCurley Constant". MathWorld.
^ Weisstein, Eric W. "Apollonian Gasket". MathWorld.
^ Weisstein, Eric W. "Backhouse's Constant". MathWorld.
^ Weisstein, Eric W. "Random Fibonacci Sequence". MathWorld.
^ Weisstein, Eric W. "e". MathWorld.
^ Weisstein, Eric W. "Komornik-Loreti Constant". MathWorld.
^ Weisstein, Eric W. "Paper Folding Constant". MathWorld.
^ Weisstein, Eric W. "Artin's Constant". MathWorld.
^ Weisstein, Eric W. "MRB Constant". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "SomossQuadraticRecurrence Constant". MathWorld.
^ Jump up to: ^a ^b Weisstein, Eric W. "Foias Constant". MathWorld.
^ Weisstein, Eric W. "Log Gamma Function". MathWorld.
^ Weisstein, Eric W. "Polygon Inscribing". MathWorld.
^ Weisstein, Eric W. "Thue-Morse Constant". MathWorld.
^ Weisstein, Eric W. "Heath-Brown-Moroz Constant". MathWorld.
^ Weisstein, Eric W. "List of mathematical constants". MathWorld.
^ Weisstein, Eric W. "Du Bois Reymond Constants". MathWorld.
^ Weisstein, Eric W. "Stephen's Constant". MathWorld.
^ Weisstein, Eric W. "Euler Product". MathWorld.
^ Weisstein, Eric W. "Copeland-Erdos Constant". MathWorld.
^ Weisstein, Eric W. "Pascal's Triangle". MathWorld.
^ Weisstein, Eric W. "Landau-Ramanujan Constant". MathWorld.
^ Weisstein, Eric W. "Convergent Series". MathWorld.
^ Weisstein, Eric W. "Prince Rupert's Cube". MathWorld.
^ Weisstein, Eric W. "Glaisher-Kinkelin Constant". MathWorld.

Site OEIS Wiki[]

^ MRB constant

Bibliography[]

Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 2013-06-05. English translation by Catriona and David Lischka.
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

External links[]

[3] 1 can be given as a primitive notion within Peano arithmetic. Alternatively, 0 can be a primitive notion in Peano arithmetic and 1 defined as the successor to 0. This article uses the former definition for pedagogical and chronological simplicity.

[25] Both $i$ and $- i$ are roots of this equation, though neither root is truly "positive" nor more fundamental than the other as they are algebraically equivalent. The distinction between signs of $i$ and $- i$ is in some ways arbitrary, but a useful notational device. See imaginary unit for more information.

[31] Can also be defined by the infinite series ${\textstyle \sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+\cdots }$

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[10] Fowler and Robson, p. 368. Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection Archived 2012-08-13 at the Wayback Machine High resolution photographs, descriptions, and analysis of the root(2) tablet (YBC 7289) from the Yale Babylonian Collection

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[245] RICHARD J. MATHAR (2010). "NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(I pi x)x^1/x BETWEEN 1 AND INFINITY". arXiv:0912.3844 [math.CA].

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[:45-250] Jesus Guillera; Jonathan Sondow (2008). "Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent". The Ramanujan Journal. 16 (3): 247–270. arXiv:math/0506319. doi:10.1007/s11139-007-9102-0. S2CID 119131640.

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[:22-263] Jump up to: ^a ^b Steven Finch (2014). Errata and Addenda to Mathematical Constants (PDF). Harvard.edu. p. 53. Archived from the original (PDF) on 2016-03-16. Retrieved 2013-12-17.

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[4] 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. "Delian Constant". MathWorld.

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

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

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

[41] Weisstein, Eric W. "Sophomore's Dream". MathWorld.

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

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

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

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

[:4-57] Weisstein, Eric W. "Gauss's Constant". MathWorld.

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

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

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

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

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

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

[:1-79] Jump up to: ^a ^b Weisstein, Eric W. "Dottie Number". MathWorld.

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

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

[:3-88] Jump up to: ^a ^b Weisstein, Eric W. "Relatively Prime". MathWorld.

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

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

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

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

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

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

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

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

[118] Weisstein, Eric W. "Mandelbrot Set". MathWorld.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[Feigenbaum_Constant-181] Jump up to: ^a ^b Weisstein, Eric W. "Feigenbaum Constant". MathWorld.

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

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

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

[195] Weisstein, Eric W. "Cantor Set". MathWorld.

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

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

[:6-207] Jump up to: ^a ^b Weisstein, Eric W. "Chebyshev Constants". MathWorld.

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

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

[Brun's_Constant-216] Jump up to: ^a ^b Weisstein, Eric W. "Brun's Constant". MathWorld.

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

[223] Weisstein, Eric W. "Apollonian Gasket". MathWorld.

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

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

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

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

[Paper_Folding_Constant-239] Weisstein, Eric W. "Paper Folding Constant". MathWorld.

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

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

[:2-251] Jump up to: ^a ^b Weisstein, Eric W. "SomossQuadraticRecurrence Constant". MathWorld.

[Foias-254] Jump up to: ^a ^b Weisstein, Eric W. "Foias Constant". MathWorld.

[258] Weisstein, Eric W. "Log Gamma Function". MathWorld.

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

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

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

[270] Weisstein, Eric W. "List of mathematical constants". MathWorld.

[273] Weisstein, Eric W. "Du Bois Reymond Constants". MathWorld.

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

[278] Weisstein, Eric W. "Euler Product". MathWorld.

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

[284] Weisstein, Eric W. "Pascal's Triangle". MathWorld.

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

[292] Weisstein, Eric W. "Convergent Series". MathWorld.

[294] Weisstein, Eric W. "Prince Rupert's Cube". MathWorld.

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

[5] OEIS: A000796

[9] OEIS: A002193

[13] OEIS: A002194

[15] OEIS: A002163

[18] OEIS: A001622

[21] OEIS: A002580

[23] OEIS: A002581

[27] OEIS: A007493

[30] OEIS: A001113

[35] OEIS: A002162

[39] OEIS: A083648

[42] OEIS: A073009

[45] OEIS: A062539

[48] OEIS: A001620

[51] OEIS: A065442

[55] OEIS: A033259

[58] OEIS: A014549

[63] OEIS: A070769

[69] OEIS: A012245

[72] OEIS: A060295

[77] OEIS: A006752

[80] OEIS: A003957

[83] OEIS: A077761

[86] OEIS: A094692

[89] OEIS: A059956

[92] OEIS: A080130

[95] OEIS: A103710

[99] OEIS: A002117

[103] OEIS: A039661

[107] OEIS: A111003

[110] OEIS: A131988

[113] OEIS: A062089

[116] OEIS: A072691

[119] OEIS: A098403

[122] OEIS: A143298

[125] OEIS: A073001

[127] OEIS: A005597

[130] OEIS: A060006

[133] OEIS: A081760

[136] OEIS: A084945

[139] OEIS: A065493

[142] OEIS: A033307

[145] OEIS: A007507

[148] OEIS: A002210

[151] OEIS: A100199

[154] OEIS: A086702

[157] OEIS: A051021

[:1-160] Jump up to: ^a ^b OEIS: A073003

[161] OEIS: A163973

[162] OEIS: A163973

[164] OEIS: A195696

[168] OEIS: A086819

[171] OEIS: A118273

[174] OEIS: A033150

[176] OEIS: A113476

[179] OEIS: A086237

[182] OEIS: A006890

[185] OEIS: A100264

[188] OEIS: A058655

[191] OEIS: A073012

[193] OEIS: A006891

[:3-196] Jump up to: ^a ^b OEIS: A102525

[200] OEIS: A179260

[204] OEIS: A073011

[208] OEIS: A249205

[211] OEIS: A014715

[:2-214] Jump up to: ^a ^b OEIS: A079586

[:0-217] Jump up to: ^a ^b OEIS: A065421

[220] OEIS: A085849

[224] OEIS: A052483

[227] OEIS: A072508

[230] OEIS: A078416

[233] OEIS: A068996

[236] OEIS: A055060

[240] OEIS: A143347

[243] OEIS: A005596

[249] OEIS: A037077

[252] OEIS: A065481

[255] OEIS: A085848

[256] OEIS: A085846

[259] OEIS: A075700

[262] OEIS: A085365

[265] OEIS: A014571

[268] OEIS: A118228

[271] OEIS: A243277

[274] OEIS: A062546

[277] OEIS: A065478

[279] OEIS: A175639

[282] OEIS: A033308

[285] OEIS: A020857

[288] OEIS: A064533

[290] OEIS: A213007

[293] OEIS: A115563

[295] OEIS: A243309

[297] OEIS: A074962

[248] MRB constant

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