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] 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.

The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols in the right hand column can be found by clicking on them.

List

Name	Symbol	Decimal expansion	Formula	Year	Set
One	1	1		Prehistory	${\displaystyle \mathbb {N} }$
Two	2	2		Prehistory	${\displaystyle \mathbb {N} }$
One half	1/2	0.5		Prehistory	${\displaystyle \mathbb {Q} }$
Pi	${\displaystyle \pi }$	3.14159 26535 89793 23846 ^[Mw 1]^[OEIS 1]	Ratio of a circle's circumference to its diameter.	1900 to 1600 BCE ^[2]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Tau (mathematical constant)	${\displaystyle \tau }$	6.28318 53071 79586 47692^[3]^[OEIS 2]	Ratio of a circle's circumference to its radius. Equivalent to ${\displaystyle 2\pi }$	1900 to 1600 BCE ^[2]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Square root of 2, Pythagoras constant.^[4]	${\displaystyle {\sqrt {2}}}$	1.41421 35623 73095 04880 ^[Mw 2]^[OEIS 3]	Positive root of ${\displaystyle x^{2}=2}$	1800 to 1600 BCE^[5]	${\displaystyle \mathbb {A} }$
Square root of 3, Theodorus' constant^[6]	${\displaystyle {\sqrt {3}}}$	1.73205 08075 68877 29352 ^[Mw 3]^[OEIS 4]	Positive root of ${\displaystyle x^{2}=3}$	465 to 398 BCE	${\displaystyle \mathbb {A} }$
Square root of 5^[7]	${\displaystyle {\sqrt {5}}}$	2.23606 79774 99789 69640 ^[OEIS 5]	Positive root of ${\displaystyle x^{2}=5}$		${\displaystyle \mathbb {A} }$
Phi, Golden ratio^[8]	${\displaystyle \varphi }$  or ${\displaystyle \phi }$	1.61803 39887 49894 84820 ^[Mw 4]^[OEIS 6]	${\displaystyle {\frac {1+{\sqrt {5}}}{2}}}$	~300 BCE	${\displaystyle \mathbb {A} }$
Silver ratio^[9]	${\displaystyle \delta _{S}}$	2.41421 35623 73095 04880 ^[Mw 5]^[OEIS 7]	${\displaystyle {\sqrt {2}}+1}$	~300 BCE	${\displaystyle \mathbb {A} }$
Zero	0	0		300 to 100 BCE^[10]	${\displaystyle \mathbb {Z} }$
Negative one	−1	−1		300 to 200 BCE	${\displaystyle \mathbb {Z} }$
Cube root of 2	${\displaystyle {\sqrt[{3}]{2}}}$	1.25992 10498 94873 16476 ^[Mw 6]^[OEIS 8]	Real root of ${\displaystyle x^{3}=2}$	46 to 120 CE^[11]	${\displaystyle \mathbb {A} }$
Cube root of 3	${\displaystyle {\sqrt[{3}]{3}}}$	1.44224 95703 07408 38232 ^[OEIS 9]	Real root of ${\displaystyle x^{3}=3}$		${\displaystyle \mathbb {A} }$
Twelfth root of 2^[12]	${\displaystyle {\sqrt[{12}]{2}}}$	1.05946 30943 59295 26456 ^[OEIS 10]	Real root of ${\displaystyle x^{12}=2}$		${\displaystyle \mathbb {A} }$
Supergolden ratio^[13]	${\displaystyle \psi }$	1.46557 12318 76768 02665 ^[OEIS 11]	${\displaystyle {\frac {1+{\sqrt[{3}]{\frac {29+3{\sqrt {93}}}{2}}}+{\sqrt[{3}]{\frac {29-3{\sqrt {93}}}{2}}}}{3}}}$  Real root of ${\displaystyle x^{3}=x^{2}+1}$		${\displaystyle \mathbb {A} }$
Imaginary unit^[14]	${\displaystyle i}$	0 + 1i	Either of the two roots of ${\displaystyle x^{2}=-1}$ ^[nb 1]	1501 to 1576	${\displaystyle \mathbb {C} }$
Connective constant for the hexagonal lattice^[15]^[16]	${\displaystyle \mu }$	1.84775 90650 22573 51225 ^[Mw 7]^[OEIS 12]	${\displaystyle {\sqrt {2+{\sqrt {2}}}}}$ , as a root of the polynomial ${\displaystyle x^{4}-4x^{2}+2=0}$	1593^[OEIS 12]	${\displaystyle \mathbb {A} }$
Kepler–Bouwkamp constant^[17]	${\displaystyle K'}$	0.11494 20448 53296 20070 ^[Mw 8]^[OEIS 13]	${\displaystyle \prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...}$	1596^[OEIS 13]
Wallis's constant		2.09455 14815 42326 59148 ^[Mw 9]^[OEIS 14]	${\displaystyle {\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}}$  Real root of ${\displaystyle x^{3}-2x-5=0}$	1616 to 1703	${\displaystyle \mathbb {A} }$
Euler's number^[18]	${\displaystyle e}$	2.71828 18284 59045 23536 ^[Mw 10]^[OEIS 15]	${\displaystyle \lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}=\sum _{n=0}^{\infty }{\frac {1}{n!}}=1+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}\cdots }$	1618^[19]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Natural logarithm of 2^[20]	${\displaystyle \ln 2}$	0.69314 71805 59945 30941 ^[Mw 11]^[OEIS 16]	Real root of ${\displaystyle e^{x}=2}$  ${\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+\cdots }$	1619 ^[21] & 1668^[22]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Lemniscate constant^[23]	${\displaystyle \varpi }$	2.62205 75542 92119 81046 ^[Mw 12]^[OEIS 17]	${\displaystyle \pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {1}{4}}\right)^{2}}}$  where ${\displaystyle G}$  is Gauss's constant	1718 to 1798	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Euler's constant	${\displaystyle \gamma }$	0.57721 56649 01532 86060 ^[Mw 13]^[OEIS 18]	${\displaystyle \lim _{n\to \infty }\left(-\log n+\sum _{k=1}^{n}{\frac {1}{k}}\right)=\int _{1}^{\infty }\left(-{\frac {1}{x}}+{\frac {1}{\lfloor x\rfloor }}\right)\,dx}$	1735
Erdős–Borwein constant^[24]	${\displaystyle E}$	1.60669 51524 15291 76378 ^[Mw 14]^[OEIS 19]	${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!\cdots }$	1749^[25]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Omega constant	${\displaystyle \Omega }$	0.56714 32904 09783 87299 ^[Mw 15]^[OEIS 20]	${\displaystyle W(1)={\frac {1}{\pi }}\int _{0}^{\pi }\log \left(1+{\frac {\sin t}{t}}e^{t\cot t}\right)dt}$  where W is the Lambert W function	1758 & 1783	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Apéry's constant^[26]	${\displaystyle \zeta (3)}$	1.20205 69031 59594 28539 ^[Mw 16]^[OEIS 21]	${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots }$	1780^[OEIS 21]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Laplace limit^[27]		0.66274 34193 49181 58097 ^[Mw 17]^[OEIS 22]	Real root of ${\displaystyle {\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1}$	~1782	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Ramanujan–Soldner constant^[28]^[29]	${\displaystyle \mu }$	1.45136 92348 83381 05028 ^[Mw 18]^[OEIS 23]	${\displaystyle \mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0}$ ; root of the logarithmic integral function.	1792^[OEIS 23]
Gauss's constant^[30]	${\displaystyle G}$	0.83462 68416 74073 18628 ^[Mw 19]^[OEIS 24]	${\displaystyle {\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {\Gamma ({\frac {1}{4}})^{2}}{2{\sqrt {2\pi ^{3}}}}}={\frac {2}{\pi }}\int _{0}^{1}{\frac {dx}{\sqrt {1-x^{4}}}}}$  where agm is the arithmetic–geometric mean	1799^[31]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Second Hermite constant^[32]	${\displaystyle \gamma _{2}}$	1.15470 05383 79251 52901 ^[Mw 20]^[OEIS 25]	${\displaystyle {\frac {2}{\sqrt {3}}}}$	1822 to 1901	${\displaystyle \mathbb {A} }$
Liouville's constant^[33]	${\displaystyle L}$	0.11000 10000 00000 00000 0001 ^[Mw 21]^[OEIS 26]	${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots }$	Before 1844	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
First continued fraction constant	${\displaystyle C_{1}}$	0.69777 46579 64007 98201 ^[Mw 22]^[OEIS 27]	${\displaystyle {\tfrac {1}{1+{\tfrac {1}{2+{\tfrac {1}{3+{\tfrac {1}{4+{\tfrac {1}{5+\cdots }}}}}}}}}}}$  ${\displaystyle {\frac {I_{1}(2)}{I_{0}(2)}}}$ , where ${\displaystyle I_{\alpha }(x)}$  is the modified Bessel function	1855^[34]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Ramanujan's constant^[35]		262 53741 26407 68743 .99999 99999 99250 073 ^[Mw 23]^[OEIS 28]	${\displaystyle e^{\pi {\sqrt {163}}}}$	1859	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Glaisher–Kinkelin constant	${\displaystyle A}$	1.28242 71291 00622 63687^[Mw 24]^[OEIS 29]	${\displaystyle e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}}$	1860^[OEIS 29]
Catalan's constant^[36]^[37]^[38]	${\displaystyle G}$	0.91596 55941 77219 01505 ^[Mw 25]^[OEIS 30]	${\displaystyle \int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {dx\,dy}{1{+}x^{2}y^{2}}}=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }}$	1864
Dottie number^[39]		0.73908 51332 15160 64165 ^[Mw 26]^[OEIS 31]	Real root of ${\displaystyle \cos x=x}$	1865^[Mw 26]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Meissel–Mertens constant^[40]	${\displaystyle M}$	0.26149 72128 47642 78375 ^[Mw 27]^[OEIS 32]	${\displaystyle \lim _{n\to \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln \ln n\right)=\gamma +\sum _{p}\left(\ln \left(1-{\frac {1}{p}}\right)+{\frac {1}{p}}\right)}$  where γ is the Euler–Mascheroni constant and p is prime	1866 & 1873
Universal parabolic constant^[41]	${\displaystyle P}$	2.29558 71493 92638 07403 ^[Mw 28]^[OEIS 33]	${\displaystyle \ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arsinh} (1)+{\sqrt {2}}}$	Before 1891^[42]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Cahen's constant^[43]	${\displaystyle C}$	0.64341 05462 88338 02618 ^[Mw 29]^[OEIS 34]	${\displaystyle \sum _{k=1}^{\infty }{\frac {(-1)^{k}}{s_{k}-1}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{6}}-{\frac {1}{42}}+{\frac {1}{1806}}{\,\pm \cdots }}$  where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...	1891	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Gelfond's constant^[44]	${\displaystyle e^{\pi }}$	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]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Gelfond–Schneider constant^[46]	${\displaystyle 2^{\sqrt {2}}}$	2.66514 41426 90225 18865 ^[Mw 31]^[OEIS 36]		Before 1902^[OEIS 36]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Second Favard constant^[47]	${\displaystyle K_{2}}$	1.23370 05501 36169 82735 ^[Mw 32]^[OEIS 37]	${\displaystyle {\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots }$	1902 to 1965	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Golden angle^[48]	${\displaystyle g}$	2.39996 32297 28653 32223 ^[Mw 33]^[OEIS 38]	${\displaystyle {\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})}$  or ${\displaystyle 180(3-{\sqrt {5}})=137.50776\ldots }$  in degrees	1907	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Sierpiński's constant^[49]	${\displaystyle K}$	2.58498 17595 79253 21706 ^[Mw 34]^[OEIS 39]	${\displaystyle {\begin{aligned}&\pi \left(2\gamma +\ln {\frac {4\pi ^{3}}{\Gamma ({\tfrac {1}{4}})^{4}}}\right)=\pi (2\gamma +4\ln \Gamma ({\tfrac {3}{4}})-\ln \pi )\\&=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)\end{aligned}}}$	1907
Landau–Ramanujan constant^[50]	${\displaystyle K}$	0.76422 36535 89220 66299 ^[Mw 35]^[OEIS 40]	${\displaystyle {\frac {1}{\sqrt {2}}}\prod _{{p\equiv 3{\text{ mod }}4} \atop p\;{\rm {prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}\!\!={\frac {\pi }{4}}\prod _{{p\equiv 1{\text{ mod }}4} \atop p\;{\rm {prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}}$	1908^[OEIS 40]
First Nielsen–Ramanujan constant^[51]	${\displaystyle a_{1}}$	0.82246 70334 24113 21823 ^[Mw 36]^[OEIS 41]	${\displaystyle {\frac {{\zeta }(2)}{2}}={\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}\cdots }$	1909	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Gieseking constant^[52]	${\displaystyle G}$	1.01494 16064 09653 62502 ^[Mw 37]^[OEIS 42]	${\displaystyle {\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=}$  ${\displaystyle \textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)}$ .	1912
Bernstein's constant^[53]	${\displaystyle \beta }$	0.28016 94990 23869 13303 ^[Mw 38]^[OEIS 43]	${\displaystyle \lim _{n\to \infty }2nE_{2n}(f)}$ , where En(f) is the error of the best uniform approximation to a real function f(x) on the interval [−1, 1] by real polynomials of no more than degree n, and f(x) = |x|	1913
Tribonacci constant^[54]		1.83928 67552 14161 13255 ^[Mw 39]^[OEIS 44]	${\textstyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {33}}}}+{\sqrt[{3}]{19-3{\sqrt {33}}}}}{3}}={\frac {1+4\cosh \left({\frac {1}{3}}\cosh ^{-1}\left(2+{\frac {3}{8}}\right)\right)}{3}}}$  Real root of ${\displaystyle x^{3}-x^{2}-x-1=0}$	1914 to 1963	${\displaystyle \mathbb {A} }$
Brun's constant^[55]	${\displaystyle B_{2}}$	1.90216 05831 04 ^[Mw 40]^[OEIS 45]	${\displaystyle \textstyle {\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+2}})}=({\frac {1}{3}}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}})+\cdots }$  where the sum ranges over all primes p such that p + 2 is also a prime	1919^[OEIS 45]
Twin primes constant	${\displaystyle C_{2}}$	0.66016 18158 46869 57392 ^[Mw 41]^[OEIS 46]	${\displaystyle \prod _{\textstyle {p\;{\rm {prime}} \atop p\geq 3}}\left(1-{\frac {1}{(p-1)^{2}}}\right)}$	1922
Plastic number^[56]	${\displaystyle \rho }$	1.32471 79572 44746 02596 ^[Mw 42]^[OEIS 47]	${\displaystyle {\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {\sqrt {69}}{18}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {\sqrt {69}}{18}}}}}$  Real root of ${\displaystyle x^{3}=x+1}$	1924^[OEIS 47]	${\displaystyle \mathbb {A} }$
Bloch's constant^[57]	${\displaystyle B}$	${\displaystyle 0.4332\leq B\leq 0.4719}$  ^[Mw 43]^[OEIS 48]	The best known bounds are ${\displaystyle {\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}}$	1925^[OEIS 48]
Z score for the 97.5 percentile point^[58]^[59]^[60]^[61]	${\displaystyle z_{.975}}$	1.95996 39845 40054 23552 ^[Mw 44]^[OEIS 49]	${\displaystyle {\sqrt {2}}\operatorname {erf} ^{-1}(0.95)}$  where erf^−1(x) is the inverse error function Real number ${\displaystyle z}$  such that ${\displaystyle {\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975}$	1925
Landau's constant^[57]	${\displaystyle L}$	${\displaystyle 0.5<L\leq 0.54326}$  ^[Mw 45]^[OEIS 50]	The best known bounds are ${\displaystyle 0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}}$	1929
Landau's third constant^[57]	${\displaystyle A}$	${\displaystyle 0.5<A\leq 0.7853}$		1929
Prouhet–Thue–Morse constant^[62]	${\displaystyle \tau }$	0.41245 40336 40107 59778 ^[Mw 46]^[OEIS 51]	${\displaystyle \sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}={\frac {1}{4}}\left[2-\prod _{n=0}^{\infty }\left(1-{\frac {1}{2^{2^{n}}}}\right)\right]}$  where ${\displaystyle {t_{n}}}$  is the n^th term of the Thue–Morse sequence	1929^[OEIS 51]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Golomb–Dickman constant^[63]	${\displaystyle \lambda }$	0.62432 99885 43550 87099 ^[Mw 47]^[OEIS 52]	${\displaystyle \int _{0}^{1}e^{\mathrm {Li} (t)}dt=\int _{0}^{\infty }{\frac {\rho (t)}{t+2}}dt}$  where Li(t) is the logarithmic integral, and ρ(t) is the Dickman function	1930 & 1964
Constant related to the asymptotic behavior of Lebesgue constants^[64]	${\displaystyle c}$	0.98943 12738 31146 95174 ^[Mw 48]^[OEIS 53]	${\displaystyle \lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)}$	1930^[Mw 48]
Feller–Tornier constant^[65]	${\displaystyle {\mathcal {C}}_{\mathrm {FT} }}$	0.66131 70494 69622 33528 ^[Mw 49]^[OEIS 54]	${\displaystyle {{\frac {1}{2}}\prod _{p{\text{ prime}}}\left(1-{\frac {2}{p^{2}}}\right)+{\frac {1}{2}}}={\frac {3}{\pi ^{2}}}\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p^{2}-1}}\right)+{\frac {1}{2}}}$	1932
Base 10 Champernowne constant^[66]	${\displaystyle C_{10}}$	0.12345 67891 01112 13141 ^[Mw 50]^[OEIS 55]	Defined by concatenating representations of successive integers: 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...	1933	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Salem constant^[67]	${\displaystyle \sigma _{10}}$	1.17628 08182 59917 50654 ^[Mw 51]^[OEIS 56]	Largest real root of ${\displaystyle x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0}$	1933^[OEIS 56]	${\displaystyle \mathbb {A} }$
Khinchin's constant^[68]	${\displaystyle K_{0}}$	2.68545 20010 65306 44530 ^[Mw 52]^[OEIS 57]	${\displaystyle \prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\log _{2}(n)}}$	1934
Lévy's constant (1)^[69]	${\displaystyle \beta }$	1.18656 91104 15625 45282 ^[Mw 53]^[OEIS 58]	${\displaystyle {\frac {\pi ^{2}}{12\,\ln 2}}}$	1935
Lévy's constant (2)^[70]	${\displaystyle e^{\beta }}$	3.27582 29187 21811 15978 ^[Mw 54]^[OEIS 59]	${\displaystyle e^{\pi ^{2}/(12\ln 2)}}$	1936
Copeland–Erdős constant^[71]	${\displaystyle {\mathcal {C}}_{CE}}$	0.23571 11317 19232 93137 ^[Mw 55]^[OEIS 60]	Defined by concatenating representations of successive prime numbers: 0.2 3 5 7 11 13 17 19 23 29 31 37 ...	1946^[OEIS 60]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Mills' constant^[72]	${\displaystyle A}$	1.30637 78838 63080 69046 ^[Mw 56]^[OEIS 61]	Smallest positive real number A such that ${\displaystyle \lfloor A^{3^{n}}\rfloor }$  is prime for all positive integers n	1947
Gompertz constant^[73]	${\displaystyle \delta }$	0.59634 73623 23194 07434 ^[Mw 57]^[OEIS 62]	${\displaystyle \int _{0}^{\infty }\!\!{\frac {e^{-x}}{1+x}}\,dx=\!\!\int _{0}^{1}\!\!{\frac {dx}{1-\ln x}}={\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {2}{1+{\tfrac {2}{1+{\tfrac {3}{1+3{/\cdots }}}}}}}}}}}}}}$	Before 1948^[OEIS 62]
de Bruijn–Newman constant	${\displaystyle \Lambda }$	${\displaystyle 0\leq \Lambda \leq 0.2}$	The number Λ where for where ${\displaystyle H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du}$  has real zeros if and only if λ ≥ Λ. where ${\displaystyle \Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}}$ .	1950
Van der Pauw constant	${\displaystyle {\frac {\pi }{\ln 2}}}$	4.53236 01418 27193 80962 ^[OEIS 63]		Before 1958^[OEIS 64]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Magic angle^[74]	${\displaystyle \theta _{\mathrm {m} }}$	0.95531 66181 245092 78163 ^[OEIS 65]	${\displaystyle \arctan {\sqrt {2}}=\arccos {\tfrac {1}{\sqrt {3}}}\approx \textstyle {54.7356}^{\circ }}$	Before 1959^[75]^[74]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Artin's constant^[76]	${\displaystyle C_{\mathrm {Artin} }}$	0.37395 58136 19202 28805 ^[Mw 58]^[OEIS 66]	${\displaystyle \prod _{p{\text{ prime}}}\left(1-{\frac {1}{p(p-1)}}\right)}$	Before 1961^[OEIS 66]
Porter's constant^[77]	${\displaystyle C}$	1.46707 80794 33975 47289 ^[Mw 59]^[OEIS 67]	${\displaystyle {\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}}$  where γ is the Euler–Mascheroni constant and ζ '(2) is the derivative of the Riemann zeta function evaluated at s = 2	1961^[OEIS 67]
Lochs constant^[78]	${\displaystyle L}$	0.97027 01143 92033 92574 ^[Mw 60]^[OEIS 68]	${\displaystyle {\frac {6\ln 2\ln 10}{\pi ^{2}}}}$	1964
DeVicci's tesseract constant		1.00743 47568 84279 37609 ^[OEIS 69]	The largest cube that can pass through in an 4D hypercube. Positive root of ${\displaystyle 4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0}$	1966^[OEIS 69]	${\displaystyle \mathbb {A} }$
Lieb's square ice constant^[79]		1.53960 07178 39002 03869 ^[Mw 61]^[OEIS 70]	${\displaystyle \left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}}$	1967	${\displaystyle \mathbb {A} }$
Niven's constant^[80]	${\displaystyle C}$	1.70521 11401 05367 76428 ^[Mw 62]^[OEIS 71]	${\displaystyle 1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)}$	1969
Stephens' constant^[81]		0.57595 99688 92945 43964 ^[Mw 63]^[OEIS 72]	${\displaystyle \prod _{p{\text{ prime}}}\left(1-{\frac {p}{p^{3}-1}}\right)}$	1969^[OEIS 72]
Regular paperfolding sequence^[82]^[83]	${\displaystyle P}$	0.85073 61882 01867 26036 ^[Mw 64]^[OEIS 73]	${\displaystyle \sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}}$	1970^[OEIS 73]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Reciprocal Fibonacci constant^[84]	${\displaystyle \psi }$	3.35988 56662 43177 55317 ^[Mw 65]^[OEIS 74]	${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots }$  where Fn is the n^th Fibonacci number	1974^[OEIS 74]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Chvátal–Sankoff constant for the binary alphabet	${\displaystyle \gamma _{2}}$	${\displaystyle 0.788071\leq \gamma _{2}\leq 0.826280}$	${\displaystyle \lim _{n\to \infty }{\frac {\operatorname {E} [\lambda _{n,2}]}{n}}}$  where E[λn,2] is the expected longest common subsequence of two random length-n binary strings	1975
Feigenbaum constant δ ^[85]	${\displaystyle \delta }$	4.66920 16091 02990 67185 ^[Mw 66]^[OEIS 75]	${\displaystyle \lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}}$  where the sequence xn is given by ${\displaystyle x_{n+1}=ax_{n}(1-x_{n})}$	1975
Chaitin's constants ^[86]	${\displaystyle \Omega }$	In general they are uncomputable numbers. But one such number is 0.00787 49969 97812 3844. ^[Mw 67]^[OEIS 76]	${\displaystyle \sum _{p\in P}2^{-|p|}}$  p: Halted program |p|: Size in bits of program p P: Domain of all programs that stop. See also: Halting problem	1975	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Robbins constant^[87]	${\displaystyle \Delta (3)}$	0.66170 71822 67176 23515 ^[Mw 68]^[OEIS 77]	${\displaystyle {\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}}$	1977^[OEIS 77]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Weierstrass constant ^[88]		0.47494 93799 87920 65033 ^[Mw 69]^[OEIS 78]	${\displaystyle {\frac {2^{5/4}{\sqrt {\pi }}\,e^{\pi /8}}{\Gamma ({\frac {1}{4}})^{2}}}}$	Before 1978^[89]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Fransén–Robinson constant^[90]	${\displaystyle F}$	2.80777 02420 28519 36522 ^[Mw 70]^[OEIS 79]	${\displaystyle \int _{0}^{\infty }{\frac {dx}{\Gamma (x)}}=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx}$	1978
Feigenbaum constant α^[91]	${\displaystyle \alpha }$	2.50290 78750 95892 82228 ^[Mw 66]^[OEIS 80]	Ratio between the width of a tine and the width of one of its two subtines in a bifurcation diagram	1979
Second du Bois-Reymond constant^[92]	${\displaystyle C_{2}}$	0.19452 80494 65325 11361 ^[Mw 71]^[OEIS 81]	${\displaystyle {\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{2}}\right|\,dt-1}$	1983^[OEIS 81]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Erdős–Tenenbaum–Ford constant	${\displaystyle \delta }$	0.08607 13320 55934 20688 ^[OEIS 82]	${\displaystyle 1-{\frac {1+\log \log 2}{\log 2}}}$	1984
Conway's constant^[93]	${\displaystyle \lambda }$	1.30357 72690 34296 39125 ^[Mw 72]^[OEIS 83]	Real root of the polynomial: ${\displaystyle {\begin{smallmatrix}x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}}$	1987	${\displaystyle \mathbb {A} }$
Hafner–Sarnak–McCurley constant^[94]	${\displaystyle \sigma }$	0.35323 63718 54995 98454 ^[Mw 73]^[OEIS 84]	${\displaystyle \prod _{p{\text{ prime}}}{\left(1-\left(1-\prod _{n\geq 1}\left(1-{\frac {1}{p^{n}}}\right)\right)^{2}\right)}\!}$	1991^[OEIS 84]
Backhouse's constant^[95]	${\displaystyle B}$	1.45607 49485 82689 67139 ^[Mw 74]^[OEIS 85]	${\displaystyle \lim _{k\to \infty }\left|{\frac {q_{k+1}}{q_{k}}}\right\vert \quad \scriptstyle {\text{where:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty }q_{k}x^{k}}$  ${\displaystyle P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots }$ where pk is the k^th prime number	1995
Viswanath constant^[96]		1.13198 82487 943 ^[Mw 75]^[OEIS 86]	${\displaystyle \lim _{n\to \infty }|f_{n}|^{\frac {1}{n}}}$       where fn = fn−1 ± fn−2, where the signs + or − are chosen at random with equal probability 1/2	1997
Komornik–Loreti constant^[97]	${\displaystyle q}$	1.78723 16501 82965 93301 ^[Mw 76]^[OEIS 87]	Real number ${\displaystyle q}$  such that ${\displaystyle 1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}}$ , or ${\displaystyle \prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0}$  where tk is the k^th term of the Thue–Morse sequence	1998	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Embree–Trefethen constant	${\displaystyle \beta ^{\star }}$	0.70258		1999
Heath-Brown–Moroz constant^[98]	${\displaystyle C}$	0.00131 76411 54853 17810 ^[Mw 77]^[OEIS 88]	${\displaystyle \prod _{p{\text{ prime}}}\left(1-{\frac {1}{p}}\right)^{7}\left(1+{\frac {7p+1}{p^{2}}}\right)}$	1999^[OEIS 88]
MRB constant^[99]^[100]^[101]	${\displaystyle S}$	0.18785 96424 62067 12024 ^[Mw 78]^[Ow 1]^[OEIS 89]	${\displaystyle \sum _{n=1}^{\infty }(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots }$	1999
Prime constant^[102]	${\displaystyle \rho }$	0.41468 25098 51111 66024 ^[OEIS 90]	${\displaystyle \sum _{p{\text{ prime}}}{\frac {1}{2^{p}}}={\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{32}}+\cdots }$	1999^[OEIS 90]	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$
Somos' quadratic recurrence constant^[103]	${\displaystyle \sigma }$	1.66168 79496 33594 12129 ^[Mw 79]^[OEIS 91]	${\displaystyle \prod _{n=1}^{\infty }n^{{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots }$	1999^[Mw 79]
Foias constant^[104]	${\displaystyle \alpha }$	1.18745 23511 26501 05459 ^[Mw 80]^[OEIS 92]	${\displaystyle x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ for }}n=1,2,3,\ldots }$  Foias constant is the unique real number such that if x1 = α then the sequence diverges to infinity	2000
Logarithmic capacity of the unit disk^[105]^[106]		0.59017 02995 08048 11302 ^[Mw 81]^[OEIS 93]	${\displaystyle {\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}}$	Before 2003^[OEIS 93]	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$
Taniguchi constant^[81]		0.67823 44919 17391 97803 ^[Mw 82]^[OEIS 94]	${\displaystyle \prod _{p{\text{ prime}}}\left(1-{\frac {3}{p^{3}}}+{\frac {2}{p^{4}}}+{\frac {1}{p^{5}}}-{\frac {1}{p^{6}}}\right)}$	Before 2005^[81]

Mathematical constants sorted by their representations as continued fractions

The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are known.

Name	Symbol	Set	Decimal expansion	Continued fraction	Notes
Zero	0	${\displaystyle \mathbb {Z} }$	0.00000 00000	[0; ]
Golomb–Dickman constant	${\displaystyle \lambda }$		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. Weisstein noted that the continued fraction has an unusually large number of 1s.^[Mw 83]
Cahen's constant	${\displaystyle C_{2}}$	${\displaystyle \mathbb {R} \setminus \mathbb {A} }$	0.64341 05463	[0; 1, 1, 1, 2^2, 3^2, 13^2, 129^2, 25298^2, 420984147^2, 269425140741515486^2, …] ^[OEIS 96]	All terms are squares and truncated at 10 terms due to large size. Davison and Shallit used the continued fraction expansion to prove that the constant is transcendental.
Euler–Mascheroni constant	${\displaystyle \gamma }$		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]	Using the continued fraction expansion, it was shown that if γ is rational, its denominator must exceed 10^244663.
First continued fraction constant	${\displaystyle C_{1}}$	${\displaystyle \mathbb {R} \setminus \mathbb {Q} }$	0.69777 46579	[0; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …]	Equal to the ratio ${\displaystyle I_{1}(2)/I_{0}(2)}$  of modified Bessel functions of the first kind evaluated at 2.
Catalan's constant	${\displaystyle G}$ November 19, 2023 Latest articles January 01, 1970 Stade Vélodrome de Rocourt January 01, 1970 Stade de Marchan January 01, 1970 Stade des Costieres January 01, 1970 Stadium Authority of the City of Pittsburgh January 01, 1970 Stadium Happy 8 Jakarta January 01, 1970 Stadium Metallurg 1st District January 01, 1970 Stadia (unit of length) January 01, 1970 Stadio Centro d'Italia - Manlio Scopigno January 01, 1970 Stadio Diego Armando Maradona January 01, 1970 Stadio San Vito Most Read January 01, 1970 Mateusz Kościukiewicz January 01, 1970 Mathadana January 01, 1970 Mathai Varghese January 01, 1970 Mathare United January 01, 1970 Matheus Coradini Vivian list, mathematical, constants, mathematical, constant, number, whose, value, fixed, unambiguous, definition, often, referred, symbol, alphabet, letter, mathematicians, names, facilitate, using, across, multiple, mathematical, problems, example, constant, defin. 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 For example the constant p 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 The column headings may be clicked to sort the table alphabetically by decimal value or by set Explanations of the symbols in the right hand column can be found by clicking on them Contents 1 List 2 Mathematical constants sorted by their representations as continued fractions 3 Sequences of constants 4 See also 5 Notes 6 References 6 1 Site MathWorld Wolfram com 6 2 Site OEIS org 6 3 Site OEIS Wiki 7 Bibliography 8 Further reading 9 External linksList editName Symbol Decimal expansion Formula Year SetOne 1 1 Prehistory N displaystyle mathbb N nbsp Two 2 2 Prehistory N displaystyle mathbb N nbsp One half 1 2 0 5 Prehistory Q displaystyle mathbb Q nbsp Pi p displaystyle pi nbsp 3 14159 26535 89793 23846 Mw 1 OEIS 1 Ratio of a circle s circumference to its diameter 1900 to 1600 BCE 2 R A displaystyle mathbb R setminus mathbb A nbsp Tau mathematical constant t displaystyle tau nbsp 6 28318 53071 79586 47692 3 OEIS 2 Ratio of a circle s circumference to its radius Equivalent to 2 p displaystyle 2 pi nbsp 1900 to 1600 BCE 2 R A displaystyle mathbb R setminus mathbb A nbsp Square root of 2 Pythagoras constant 4 2 displaystyle sqrt 2 nbsp 1 41421 35623 73095 04880 Mw 2 OEIS 3 Positive root of x 2 2 displaystyle x 2 2 nbsp 1800 to 1600 BCE 5 A displaystyle mathbb A nbsp Square root of 3 Theodorus constant 6 3 displaystyle sqrt 3 nbsp 1 73205 08075 68877 29352 Mw 3 OEIS 4 Positive root of x 2 3 displaystyle x 2 3 nbsp 465 to 398 BCE A displaystyle mathbb A nbsp Square root of 5 7 5 displaystyle sqrt 5 nbsp 2 23606 79774 99789 69640 OEIS 5 Positive root of x 2 5 displaystyle x 2 5 nbsp A displaystyle mathbb A nbsp Phi Golden ratio 8 f displaystyle varphi nbsp or ϕ displaystyle phi nbsp 1 61803 39887 49894 84820 Mw 4 OEIS 6 1 5 2 displaystyle frac 1 sqrt 5 2 nbsp 300 BCE A displaystyle mathbb A nbsp Silver ratio 9 d S displaystyle delta S nbsp 2 41421 35623 73095 04880 Mw 5 OEIS 7 2 1 displaystyle sqrt 2 1 nbsp 300 BCE A displaystyle mathbb A nbsp Zero 0 0 300 to 100 BCE 10 Z displaystyle mathbb Z nbsp Negative one 1 1 300 to 200 BCE Z displaystyle mathbb Z nbsp Cube root of 2 2 3 displaystyle sqrt 3 2 nbsp 1 25992 10498 94873 16476 Mw 6 OEIS 8 Real root of x 3 2 displaystyle x 3 2 nbsp 46 to 120 CE 11 A displaystyle mathbb A nbsp Cube root of 3 3 3 displaystyle sqrt 3 3 nbsp 1 44224 95703 07408 38232 OEIS 9 Real root of x 3 3 displaystyle x 3 3 nbsp A displaystyle mathbb A nbsp Twelfth root of 2 12 2 12 displaystyle sqrt 12 2 nbsp 1 05946 30943 59295 26456 OEIS 10 Real root of x 12 2 displaystyle x 12 2 nbsp A displaystyle mathbb A nbsp Supergolden ratio 13 ps displaystyle psi nbsp 1 46557 12318 76768 02665 OEIS 11 1 29 3 93 2 3 29 3 93 2 3 3 displaystyle frac 1 sqrt 3 frac 29 3 sqrt 93 2 sqrt 3 frac 29 3 sqrt 93 2 3 nbsp Real root of x 3 x 2 1 displaystyle x 3 x 2 1 nbsp A displaystyle mathbb A nbsp Imaginary unit 14 i displaystyle i nbsp 0 1i Either of the two roots of x 2 1 displaystyle x 2 1 nbsp nb 1 1501 to 1576 C displaystyle mathbb C nbsp Connective constant for the hexagonal lattice 15 16 m displaystyle mu nbsp 1 84775 90650 22573 51225 Mw 7 OEIS 12 2 2 displaystyle sqrt 2 sqrt 2 nbsp as a root of the polynomial x 4 4 x 2 2 0 displaystyle x 4 4x 2 2 0 nbsp 1593 OEIS 12 A displaystyle mathbb A nbsp Kepler Bouwkamp constant 17 K displaystyle K nbsp 0 11494 20448 53296 20070 Mw 8 OEIS 13 n 3 cos p n cos p 3 cos p 4 cos p 5 displaystyle 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 nbsp 1596 OEIS 13 Wallis s constant 2 09455 14815 42326 59148 Mw 9 OEIS 14 45 1929 18 3 45 1929 18 3 displaystyle sqrt 3 frac 45 sqrt 1929 18 sqrt 3 frac 45 sqrt 1929 18 nbsp Real root of x 3 2 x 5 0 displaystyle x 3 2x 5 0 nbsp 1616 to 1703 A displaystyle mathbb A nbsp Euler s number 18 e displaystyle e nbsp 2 71828 18284 59045 23536 Mw 10 OEIS 15 lim n 1 1 n n n 0 1 n 1 1 1 1 2 1 3 displaystyle 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 nbsp 1618 19 R A displaystyle mathbb R setminus mathbb A nbsp Natural logarithm of 2 20 ln 2 displaystyle ln 2 nbsp 0 69314 71805 59945 30941 Mw 11 OEIS 16 Real root of e x 2 displaystyle e x 2 nbsp n 1 1 n 1 n 1 1 1 2 1 3 1 4 displaystyle sum n 1 infty frac 1 n 1 n frac 1 1 frac 1 2 frac 1 3 frac 1 4 cdots nbsp 1619 21 amp 1668 22 R A displaystyle mathbb R setminus mathbb A nbsp Lemniscate constant 23 ϖ displaystyle varpi nbsp 2 62205 75542 92119 81046 Mw 12 OEIS 17 p G 4 2 p G 5 4 2 1 4 2 p G 1 4 2 displaystyle 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 nbsp where G displaystyle G nbsp is Gauss s constant 1718 to 1798 R A displaystyle mathbb R setminus mathbb A nbsp Euler s constant g displaystyle gamma nbsp 0 57721 56649 01532 86060 Mw 13 OEIS 18 lim n log n k 1 n 1 k 1 1 x 1 x d x displaystyle 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 nbsp 1735Erdos Borwein constant 24 E displaystyle E nbsp 1 60669 51524 15291 76378 Mw 14 OEIS 19 n 1 1 2 n 1 1 1 1 3 1 7 1 15 displaystyle sum n 1 infty frac 1 2 n 1 frac 1 1 frac 1 3 frac 1 7 frac 1 15 cdots nbsp 1749 25 R Q displaystyle mathbb R setminus mathbb Q nbsp Omega constant W displaystyle Omega nbsp 0 56714 32904 09783 87299 Mw 15 OEIS 20 W 1 1 p 0 p log 1 sin t t e t cot t d t displaystyle W 1 frac 1 pi int 0 pi log left 1 frac sin t t e t cot t right dt nbsp where W is the Lambert W function 1758 amp 1783 R A displaystyle mathbb R setminus mathbb A nbsp Apery s constant 26 z 3 displaystyle zeta 3 nbsp 1 20205 69031 59594 28539 Mw 16 OEIS 21 n 1 1 n 3 1 1 3 1 2 3 1 3 3 1 4 3 1 5 3 displaystyle 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 nbsp 1780 OEIS 21 R Q displaystyle mathbb R setminus mathbb Q nbsp Laplace limit 27 0 66274 34193 49181 58097 Mw 17 OEIS 22 Real root of x e x 2 1 x 2 1 1 1 displaystyle frac xe sqrt x 2 1 sqrt x 2 1 1 1 nbsp 1782 R A displaystyle mathbb R setminus mathbb A nbsp Ramanujan Soldner constant 28 29 m displaystyle mu nbsp 1 45136 92348 83381 05028 Mw 18 OEIS 23 l i x 0 x d t ln t 0 displaystyle mathrm li x int 0 x frac dt ln t 0 nbsp root of the logarithmic integral function 1792 OEIS 23 Gauss s constant 30 G displaystyle G nbsp 0 83462 68416 74073 18628 Mw 19 OEIS 24 1 a g m 1 2 G 1 4 2 2 2 p 3 2 p 0 1 d x 1 x 4 displaystyle frac 1 mathrm agm 1 sqrt 2 frac Gamma frac 1 4 2 2 sqrt 2 pi 3 frac 2 pi int 0 1 frac dx sqrt 1 x 4 nbsp where agm is the arithmetic geometric mean 1799 31 R A displaystyle mathbb R setminus mathbb A nbsp Second Hermite constant 32 g 2 displaystyle gamma 2 nbsp 1 15470 05383 79251 52901 Mw 20 OEIS 25 2 3 displaystyle frac 2 sqrt 3 nbsp 1822 to 1901 A displaystyle mathbb A nbsp Liouville s constant 33 L displaystyle L nbsp 0 11000 10000 00000 00000 0001 Mw 21 OEIS 26 n 1 1 10 n 1 10 1 1 10 2 1 10 3 1 10 4 displaystyle 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 nbsp Before 1844 R A displaystyle mathbb R setminus mathbb A nbsp First continued fraction constant C 1 displaystyle C 1 nbsp 0 69777 46579 64007 98201 Mw 22 OEIS 27 1 1 1 2 1 3 1 4 1 5 displaystyle tfrac 1 1 tfrac 1 2 tfrac 1 3 tfrac 1 4 tfrac 1 5 cdots nbsp I 1 2 I 0 2 displaystyle frac I 1 2 I 0 2 nbsp where I a x displaystyle I alpha x nbsp is the modified Bessel function 1855 34 R Q displaystyle mathbb R setminus mathbb Q nbsp Ramanujan s constant 35 262 53741 26407 68743 99999 99999 99250 073 Mw 23 OEIS 28 e p 163 displaystyle e pi sqrt 163 nbsp 1859 R A displaystyle mathbb R setminus mathbb A nbsp Glaisher Kinkelin constant A displaystyle A nbsp 1 28242 71291 00622 63687 Mw 24 OEIS 29 e 1 12 z 1 e 1 8 1 2 n 0 1 n 1 k 0 n 1 k n k k 1 2 ln k 1 displaystyle 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 nbsp 1860 OEIS 29 Catalan s constant 36 37 38 G displaystyle G nbsp 0 91596 55941 77219 01505 Mw 25 OEIS 30 0 1 0 1 d x d y 1 x 2 y 2 n 0 1 n 2 n 1 2 1 1 2 1 3 2 displaystyle 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 nbsp 1864Dottie number 39 0 73908 51332 15160 64165 Mw 26 OEIS 31 Real root of cos x x displaystyle cos x x nbsp 1865 Mw 26 R A displaystyle mathbb R setminus mathbb A nbsp Meissel Mertens constant 40 M displaystyle M nbsp 0 26149 72128 47642 78375 Mw 27 OEIS 32 lim n p n 1 p ln ln n g p ln 1 1 p 1 p displaystyle 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 nbsp where g is the Euler Mascheroni constant and p is prime 1866 amp 1873Universal parabolic constant 41 P displaystyle P nbsp 2 29558 71493 92638 07403 Mw 28 OEIS 33 ln 1 2 2 arsinh 1 2 displaystyle ln 1 sqrt 2 sqrt 2 operatorname arsinh 1 sqrt 2 nbsp Before 1891 42 R A displaystyle mathbb R setminus mathbb A nbsp Cahen s constant 43 C displaystyle C nbsp 0 64341 05462 88338 02618 Mw 29 OEIS 34 k 1 1 k s k 1 1 1 1 2 1 6 1 42 1 1806 displaystyle 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 nbsp where sk is the kth term of Sylvester s sequence 2 3 7 43 1807 1891 R A displaystyle mathbb R setminus mathbb A nbsp Gelfond s constant 44 e p displaystyle e pi nbsp 23 14069 26327 79269 0057 Mw 30 OEIS 35 1 i i 2 i n 0 p n n 1 p 1 1 p 2 2 p 3 6 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 nbsp 1900 45 R A displaystyle mathbb R setminus mathbb A nbsp Gelfond Schneider constant 46 2 2 displaystyle 2 sqrt 2 nbsp 2 66514 41426 90225 18865 Mw 31 OEIS 36 Before 1902 OEIS 36 R A displaystyle mathbb R setminus mathbb A nbsp Second Favard constant 47 K 2 displaystyle K 2 nbsp 1 23370 05501 36169 82735 Mw 32 OEIS 37 p 2 8 n 0 1 2 n 1 2 1 1 2 1 3 2 1 5 2 1 7 2 displaystyle 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 nbsp 1902 to 1965 R A displaystyle mathbb R setminus mathbb A nbsp Golden angle 48 g displaystyle g nbsp 2 39996 32297 28653 32223 Mw 33 OEIS 38 2 p f 2 p 3 5 displaystyle frac 2 pi varphi 2 pi 3 sqrt 5 nbsp or 180 3 5 137 50776 displaystyle 180 3 sqrt 5 137 50776 ldots nbsp in degrees 1907 R A displaystyle mathbb R setminus mathbb A nbsp Sierpinski s constant 49 K displaystyle K nbsp 2 58498 17595 79253 21706 Mw 34 OEIS 39 p 2 g ln 4 p 3 G 1 4 4 p 2 g 4 ln G 3 4 ln p p 2 ln 2 3 ln p 2 g 4 ln G 1 4 displaystyle begin aligned amp 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 amp pi left 2 ln 2 3 ln pi 2 gamma 4 ln Gamma tfrac 1 4 right end aligned nbsp 1907Landau Ramanujan constant 50 K displaystyle K nbsp 0 76422 36535 89220 66299 Mw 35 OEIS 40 1 2 p 3 mod 4 p p r i m e 1 1 p 2 1 2 p 4 p 1 mod 4 p p r i m e 1 1 p 2 1 2 displaystyle 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 nbsp 1908 OEIS 40 First Nielsen Ramanujan constant 51 a 1 displaystyle a 1 nbsp 0 82246 70334 24113 21823 Mw 36 OEIS 41 z 2 2 p 2 12 n 1 1 n 1 n 2 1 1 2 1 2 2 1 3 2 1 4 2 displaystyle frac zeta 2 2 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 cdots nbsp 1909 R A displaystyle mathbb R setminus mathbb A nbsp Gieseking constant 52 G displaystyle G nbsp 1 01494 16064 09653 62502 Mw 37 OEIS 42 3 3 4 1 n 0 1 3 n 2 2 n 1 1 3 n 1 2 displaystyle 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 nbsp 3 3 4 1 1 2 2 1 4 2 1 5 2 1 7 2 1 8 2 1 10 2 displaystyle 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 nbsp 1912Bernstein s constant 53 b displaystyle beta nbsp 0 28016 94990 23869 13303 Mw 38 OEIS 43 lim n 2 n E 2 n f displaystyle lim n to infty 2nE 2n f nbsp where En f is the error of the best uniform approximation to a real function f x on the interval 1 1 by real polynomials of no more than degree n and f x x 1913Tribonacci constant 54 1 83928 67552 14161 13255 Mw 39 OEIS 44 1 19 3 33 3 19 3 33 3 3 1 4 cosh 1 3 cosh 1 2 3 8 3 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 nbsp Real root of x 3 x 2 x 1 0 displaystyle x 3 x 2 x 1 0 nbsp 1914 to 1963 A displaystyle mathbb A nbsp Brun s constant 55 B 2 displaystyle B 2 nbsp 1 90216 05831 04 Mw 40 OEIS 45 p 1 p 1 p 2 1 3 1 5 1 5 1 7 1 11 1 13 displaystyle 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 nbsp where the sum ranges over all primes p such that p 2 is also a prime 1919 OEIS 45 Twin primes constant C 2 displaystyle C 2 nbsp 0 66016 18158 46869 57392 Mw 41 OEIS 46 p p r i m e p 3 1 1 p 1 2 displaystyle prod textstyle p rm prime atop p geq 3 left 1 frac 1 p 1 2 right nbsp 1922Plastic number 56 r displaystyle rho nbsp 1 32471 79572 44746 02596 Mw 42 OEIS 47 1 1 1 3 3 3 1 2 69 18 3 1 2 69 18 3 displaystyle 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 nbsp Real root of x 3 x 1 displaystyle x 3 x 1 nbsp 1924 OEIS 47 A displaystyle mathbb A nbsp Bloch s constant 57 B displaystyle B nbsp 0 4332 B 0 4719 displaystyle 0 4332 leq B leq 0 4719 nbsp Mw 43 OEIS 48 The best known bounds are 3 4 2 10 4 B 3 1 2 G 1 3 G 11 12 G 1 4 displaystyle 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 nbsp 1925 OEIS 48 Z score for the 97 5 percentile point 58 59 60 61 z 975 displaystyle z 975 nbsp 1 95996 39845 40054 23552 Mw 44 OEIS 49 2 erf 1 0 95 displaystyle sqrt 2 operatorname erf 1 0 95 nbsp where erf 1 x is the inverse error function Real number z displaystyle z nbsp such that 1 2 p z e x 2 2 d x 0 975 displaystyle frac 1 sqrt 2 pi int infty z e x 2 2 mathrm d x 0 975 nbsp 1925Landau s constant 57 L displaystyle L nbsp 0 5 lt L 0 54326 displaystyle 0 5 lt L leq 0 54326 nbsp Mw 45 OEIS 50 The best known bounds are 0 5 lt L G 1 3 G 5 6 G 1 6 displaystyle 0 5 lt L leq frac Gamma frac 1 3 Gamma frac 5 6 Gamma frac 1 6 nbsp 1929Landau s third constant 57 A displaystyle A nbsp 0 5 lt A 0 7853 displaystyle 0 5 lt A leq 0 7853 nbsp 1929Prouhet Thue Morse constant 62 t displaystyle tau nbsp 0 41245 40336 40107 59778 Mw 46 OEIS 51 n 0 t n 2 n 1 1 4 2 n 0 1 1 2 2 n displaystyle sum n 0 infty frac t n 2 n 1 frac 1 4 left 2 prod n 0 infty left 1 frac 1 2 2 n right right nbsp where t n displaystyle t n nbsp is the nth term of the Thue Morse sequence 1929 OEIS 51 R A displaystyle mathbb R setminus mathbb A nbsp Golomb Dickman constant 63 l displaystyle lambda nbsp 0 62432 99885 43550 87099 Mw 47 OEIS 52 0 1 e L i t d t 0 r t t 2 d t displaystyle int 0 1 e mathrm Li t dt int 0 infty frac rho t t 2 dt nbsp where Li t is the logarithmic integral and r t is the Dickman function 1930 amp 1964Constant related to the asymptotic behavior of Lebesgue constants 64 c displaystyle c nbsp 0 98943 12738 31146 95174 Mw 48 OEIS 53 lim n L n 4 p 2 ln 2 n 1 4 p 2 k 1 2 ln k 4 k 2 1 G 1 2 G 1 2 displaystyle 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 nbsp 1930 Mw 48 Feller Tornier constant 65 C F T displaystyle mathcal C mathrm FT nbsp 0 66131 70494 69622 33528 Mw 49 OEIS 54 1 2 p prime 1 2 p 2 1 2 3 p 2 p prime 1 1 p 2 1 1 2 displaystyle frac 1 2 prod p text prime left 1 frac 2 p 2 right frac 1 2 frac 3 pi 2 prod p text prime left 1 frac 1 p 2 1 right frac 1 2 nbsp 1932Base 10 Champernowne constant 66 C 10 displaystyle C 10 nbsp 0 12345 67891 01112 13141 Mw 50 OEIS 55 Defined by concatenating representations of successive integers 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1933 R A displaystyle mathbb R setminus mathbb A nbsp Salem constant 67 s 10 displaystyle sigma 10 nbsp 1 17628 08182 59917 50654 Mw 51 OEIS 56 Largest real root of 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 nbsp 1933 OEIS 56 A displaystyle mathbb A nbsp Khinchin s constant 68 K 0 displaystyle K 0 nbsp 2 68545 20010 65306 44530 Mw 52 OEIS 57 n 1 1 1 n n 2 log 2 n displaystyle prod n 1 infty left 1 1 over n n 2 right log 2 n nbsp 1934Levy s constant 1 69 b displaystyle beta nbsp 1 18656 91104 15625 45282 Mw 53 OEIS 58 p 2 12 ln 2 displaystyle frac pi 2 12 ln 2 nbsp 1935Levy s constant 2 70 e b displaystyle e beta nbsp 3 27582 29187 21811 15978 Mw 54 OEIS 59 e p 2 12 ln 2 displaystyle e pi 2 12 ln 2 nbsp 1936Copeland Erdos constant 71 C C E displaystyle mathcal C CE nbsp 0 23571 11317 19232 93137 Mw 55 OEIS 60 Defined by concatenating representations of successive prime numbers 0 2 3 5 7 11 13 17 19 23 29 31 37 1946 OEIS 60 R Q displaystyle mathbb R setminus mathbb Q nbsp Mills constant 72 A displaystyle A nbsp 1 30637 78838 63080 69046 Mw 56 OEIS 61 Smallest positive real number A such that A 3 n displaystyle lfloor A 3 n rfloor nbsp is prime for all positive integers n 1947Gompertz constant 73 d displaystyle delta nbsp 0 59634 73623 23194 07434 Mw 57 OEIS 62 0 e x 1 x d x 0 1 d x 1 ln x 1 1 1 1 1 1 2 1 2 1 3 1 3 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 1 1 tfrac 2 1 tfrac 2 1 tfrac 3 1 3 cdots nbsp Before 1948 OEIS 62 de Bruijn Newman constant L displaystyle Lambda nbsp 0 L 0 2 displaystyle 0 leq Lambda leq 0 2 nbsp The number L where for where H l z 0 e l u 2 F u cos z u d u displaystyle H lambda z int 0 infty e lambda u 2 Phi u cos zu du nbsp has real zeros if and only if l L where F u n 1 2 p 2 n 4 e 9 u 3 p n 2 e 5 u e p n 2 e 4 u displaystyle 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 nbsp 1950Van der Pauw constant p ln 2 displaystyle frac pi ln 2 nbsp 4 53236 01418 27193 80962 OEIS 63 Before 1958 OEIS 64 R Q displaystyle mathbb R setminus mathbb Q nbsp Magic angle 74 8 m displaystyle theta mathrm m nbsp 0 95531 66181 245092 78163 OEIS 65 arctan 2 arccos 1 3 54 7356 displaystyle arctan sqrt 2 arccos tfrac 1 sqrt 3 approx textstyle 54 7356 circ nbsp Before 1959 75 74 R A displaystyle mathbb R setminus mathbb A nbsp Artin s constant 76 C A r t i n displaystyle C mathrm Artin nbsp 0 37395 58136 19202 28805 Mw 58 OEIS 66 p prime 1 1 p p 1 displaystyle prod p text prime left 1 frac 1 p p 1 right nbsp Before 1961 OEIS 66 Porter s constant 77 C displaystyle C nbsp 1 46707 80794 33975 47289 Mw 59 OEIS 67 6 ln 2 p 2 3 ln 2 4 g 24 p 2 z 2 2 1 2 displaystyle frac 6 ln 2 pi 2 left 3 ln 2 4 gamma frac 24 pi 2 zeta 2 2 right frac 1 2 nbsp where g is the Euler Mascheroni constant and z 2 is the derivative of the Riemann zeta function evaluated at s 2 1961 OEIS 67 Lochs constant 78 L displaystyle L nbsp 0 97027 01143 92033 92574 Mw 60 OEIS 68 6 ln 2 ln 10 p 2 displaystyle frac 6 ln 2 ln 10 pi 2 nbsp 1964DeVicci s tesseract constant 1 00743 47568 84279 37609 OEIS 69 The largest cube that can pass through in an 4D hypercube Positive root of 4 x 8 28 x 6 7 x 4 16 x 2 16 0 displaystyle 4x 8 28x 6 7x 4 16x 2 16 0 nbsp 1966 OEIS 69 A displaystyle mathbb A nbsp Lieb s square ice constant 79 1 53960 07178 39002 03869 Mw 61 OEIS 70 4 3 3 2 8 3 3 displaystyle left frac 4 3 right frac 3 2 frac 8 3 sqrt 3 nbsp 1967 A displaystyle mathbb A nbsp Niven s constant 80 C displaystyle C nbsp 1 70521 11401 05367 76428 Mw 62 OEIS 71 1 n 2 1 1 z n displaystyle 1 sum n 2 infty left 1 frac 1 zeta n right nbsp 1969Stephens constant 81 0 57595 99688 92945 43964 Mw 63 OEIS 72 p prime 1 p p 3 1 displaystyle prod p text prime left 1 frac p p 3 1 right nbsp 1969 OEIS 72 Regular paperfolding sequence 82 83 P displaystyle P nbsp 0 85073 61882 01867 26036 Mw 64 OEIS 73 n 0 8 2 n 2 2 n 2 1 n 0 1 2 2 n 1 1 2 2 n 2 displaystyle 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 nbsp 1970 OEIS 73 R A displaystyle mathbb R setminus mathbb A nbsp Reciprocal Fibonacci constant 84 ps displaystyle psi nbsp 3 35988 56662 43177 55317 Mw 65 OEIS 74 n 1 1 F n 1 1 1 1 1 2 1 3 1 5 1 8 1 13 displaystyle 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 nbsp where Fn is the nth Fibonacci number 1974 OEIS 74 R Q displaystyle mathbb R setminus mathbb Q nbsp Chvatal Sankoff constant for the binary alphabet g 2 displaystyle gamma 2 nbsp 0 788071 g 2 0 826280 displaystyle 0 788071 leq gamma 2 leq 0 826280 nbsp lim n E l n 2 n displaystyle lim n to infty frac operatorname E lambda n 2 n nbsp where E ln 2 is the expected longest common subsequence of two random length n binary strings 1975Feigenbaum constant d 85 d displaystyle delta nbsp 4 66920 16091 02990 67185 Mw 66 OEIS 75 lim n x n 1 x n x n 2 x n 1 displaystyle lim n to infty frac x n 1 x n x n 2 x n 1 nbsp where the sequence xn is given by x n 1 a x n 1 x n displaystyle x n 1 ax n 1 x n nbsp 1975Chaitin s constants 86 W displaystyle Omega nbsp In general they are uncomputable numbers But one such number is 0 00787 49969 97812 3844 Mw 67 OEIS 76 p P 2 p displaystyle sum p in P 2 p nbsp p Halted program p Size in bits of program p P Domain of all programs that stop See also Halting problem 1975 R A displaystyle mathbb R setminus mathbb A nbsp Robbins constant 87 D 3 displaystyle Delta 3 nbsp 0 66170 71822 67176 23515 Mw 68 OEIS 77 4 17 2 6 3 7 p 105 ln 1 2 5 2 ln 2 3 5 displaystyle frac 4 17 sqrt 2 6 sqrt 3 7 pi 105 frac ln 1 sqrt 2 5 frac 2 ln 2 sqrt 3 5 nbsp 1977 OEIS 77 R A displaystyle mathbb R setminus mathbb A nbsp Weierstrass constant 88 0 47494 93799 87920 65033 Mw 69 OEIS 78 2 5 4 p e p 8 G 1 4 2 displaystyle frac 2 5 4 sqrt pi e pi 8 Gamma frac 1 4 2 nbsp Before 1978 89 R A displaystyle mathbb R setminus mathbb A nbsp Fransen Robinson constant 90 F displaystyle F nbsp 2 80777 02420 28519 36522 Mw 70 OEIS 79 0 d x G x e 0 e x p 2 ln 2 x d x displaystyle int 0 infty frac dx Gamma x e int 0 infty frac e x pi 2 ln 2 x dx nbsp 1978Feigenbaum constant a 91 a displaystyle alpha nbsp 2 50290 78750 95892 82228 Mw 66 OEIS 80 Ratio between the width of a tine and the width of one of its two subtines in a bifurcation diagram 1979Second du Bois Reymond constant 92 C 2 displaystyle C 2 nbsp 0 19452 80494 65325 11361 Mw 71 OEIS 81 e 2 7 2 0 d d t sin t t 2 d t 1 displaystyle frac e 2 7 2 int 0 infty left frac d dt left frac sin t t right 2 right dt 1 nbsp 1983 OEIS 81 R A displaystyle mathbb R setminus mathbb A nbsp Erdos Tenenbaum Ford constant d displaystyle delta nbsp 0 08607 13320 55934 20688 OEIS 82 1 1 log log 2 log 2 displaystyle 1 frac 1 log log 2 log 2 nbsp 1984Conway s constant 93 l displaystyle lambda nbsp 1 30357 72690 34296 39125 Mw 72 OEIS 83 Real root of the polynomial x 71 x 69 2 x 68 x 67 2 x 66 2 x 65 x 64 x 63 x 62 x 61 x 60 x 59 2 x 58 5 x 57 3 x 56 2 x 55 10 x 54 3 x 53 2 x 52 6 x 51 6 x 50 x 49 9 x 48 3 x 47 7 x 46 8 x 45 8 x 44 10 x 43 6 x 42 8 x 41 5 x 40 12 x 39 7 x 38 7 x 37 7 x 36 x 35 3 x 34 10 x 33 x 32 6 x 31 2 x 30 10 x 29 3 x 28 2 x 27 9 x 26 3 x 25 14 x 24 8 x 23 7 x 21 9 x 20 3 x 19 4 x 18 10 x 17 7 x 16 12 x 15 7 x 14 2 x 13 12 x 12 4 x 11 2 x 10 5 x 9 x 7 7 x 6 7 x 5 4 x 4 12 x 3 6 x 2 3 x 6 0 displaystyle begin smallmatrix x 71 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 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 7x 6 7x 5 4x 4 12x 3 6x 2 3x 6 0 quad quad quad end smallmatrix nbsp 1987 A displaystyle mathbb A nbsp Hafner Sarnak McCurley constant 94 s displaystyle sigma nbsp 0 35323 63718 54995 98454 Mw 73 OEIS 84 p prime 1 1 n 1 1 1 p n 2 displaystyle prod p text prime left 1 left 1 prod n geq 1 left 1 frac 1 p n right right 2 right nbsp 1991 OEIS 84 Backhouse s constant 95 B displaystyle B nbsp 1 45607 49485 82689 67139 Mw 74 OEIS 85 lim k q k 1 q k where Q x 1 P x k 1 q k x k displaystyle 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 nbsp P x 1 k 1 p k x k 1 2 x 3 x 2 5 x 3 displaystyle P x 1 sum k 1 infty p k x k 1 2x 3x 2 5x 3 cdots nbsp where pk is the kth prime number 1995Viswanath constant 96 1 13198 82487 943 Mw 75 OEIS 86 lim n f n 1 n displaystyle lim n to infty f n frac 1 n nbsp where fn fn 1 fn 2 where the signs or are chosen at random with equal probability 1 2 1997Komornik Loreti constant 97 q displaystyle q nbsp 1 78723 16501 82965 93301 Mw 76 OEIS 87 Real number q displaystyle q nbsp such that 1 k 1 t k q k displaystyle 1 sum k 1 infty frac t k q k nbsp or n 0 1 1 q 2 n q 2 q 1 0 displaystyle prod n 0 infty left 1 frac 1 q 2 n right frac q 2 q 1 0 nbsp where tk is the kth term of the Thue Morse sequence 1998 R A displaystyle mathbb R setminus mathbb A nbsp Embree Trefethen constant b displaystyle beta star nbsp 0 70258 1999Heath Brown Moroz constant 98 C displaystyle C nbsp 0 00131 76411 54853 17810 Mw 77 OEIS 88 p prime 1 1 p 7 1 7 p 1 p 2 displaystyle prod p text prime left 1 frac 1 p right 7 left 1 frac 7p 1 p 2 right nbsp 1999 OEIS 88 MRB constant 99 100 101 S displaystyle S nbsp 0 18785 96424 62067 12024 Mw 78 Ow 1 OEIS 89 n 1 1 n n 1 n 1 1 1 2 2 3 3 displaystyle sum n 1 infty 1 n n 1 n 1 sqrt 1 1 sqrt 2 2 sqrt 3 3 cdots nbsp 1999Prime constant 102 r displaystyle rho nbsp 0 41468 25098 51111 66024 OEIS 90 p prime 1 2 p 1 4 1 8 1 32 displaystyle sum p text prime frac 1 2 p frac 1 4 frac 1 8 frac 1 32 cdots nbsp 1999 OEIS 90 R Q displaystyle mathbb R setminus mathbb Q nbsp Somos quadratic recurrence constant 103 s displaystyle sigma nbsp 1 66168 79496 33594 12129 Mw 79 OEIS 91 n 1 n 1 2 n 1 2 3 1 1 2 2 1 4 3 1 8 displaystyle 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 nbsp 1999 Mw 79 Foias constant 104 a displaystyle alpha nbsp 1 18745 23511 26501 05459 Mw 80 OEIS 92 x n 1 1 1 x n n for n 1 2 3 displaystyle x n 1 left 1 frac 1 x n right n text for n 1 2 3 ldots nbsp Foias constant is the unique real number such that if x1 a then the sequence diverges to infinity 2000Logarithmic capacity of the unit disk 105 106 0 59017 02995 08048 11302 Mw 81 OEIS 93 G 1 4 2 4 p 3 2 displaystyle frac Gamma tfrac 1 4 2 4 pi 3 2 nbsp Before 2003 OEIS 93 R A displaystyle mathbb R setminus mathbb A nbsp Taniguchi constant 81 0 67823 44919 17391 97803 Mw 82 OEIS 94 p prime 1 3 p 3 2 p 4 1 p 5 1 p 6 displaystyle prod p text prime left 1 frac 3 p 3 frac 2 p 4 frac 1 p 5 frac 1 p 6 right nbsp Before 2005 81 Mathematical constants sorted by their representations as continued fractions editThe following list includes the continued fractions of some constants and is sorted by their representations Continued fractions with more than 20 known terms have been truncated with an ellipsis to show that they continue Rational numbers have two continued fractions the version in this list is the shorter one Decimal representations are rounded or padded to 10 places if the values are known Name Symbol Set Decimal expansion Continued fraction NotesZero 0 Z displaystyle mathbb Z nbsp 0 00000 00000 0 Golomb Dickman constant l displaystyle lambda nbsp 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 Weisstein noted that the continued fraction has an unusually large number of 1s Mw 83 Cahen s constant C 2 displaystyle C 2 nbsp R A displaystyle mathbb R setminus mathbb A nbsp 0 64341 05463 0 1 1 1 22 32 132 1292 252982 4209841472 2694251407415154862 OEIS 96 All terms are squares and truncated at 10 terms due to large size Davison and Shallit used the continued fraction expansion to prove that the constant is transcendental Euler Mascheroni constant g displaystyle gamma nbsp 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 Using the continued fraction expansion it was shown that if g is rational its denominator must exceed 10244663 First continued fraction constant C 1 displaystyle C 1 nbsp R Q displaystyle mathbb R setminus mathbb Q nbsp 0 69777 46579 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Equal to the ratio I 1 2 I 0 2 displaystyle I 1 2 I 0 2 nbsp of modified Bessel functions of the first kind evaluated at 2 Catalan s constant G displaystyle G span, wikipedia, wiki, book, books, library, article , read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games. © Copyright 2021, All Rights Reserved  |   www.wiki3.en-us.nina.az Rss Feed SiteMap Ping DMCA Contact Us HomePage Closed Call: