משתמש:Byc63/קבועים מתמטיים

קבוע מתמטי הוא מספר מפתח שערכו קבוע על ידי הגדרה חד-משמעית, המכונה לעיתים קרובות על ידי סמל (למשל, אות), או על ידי שמות של מתמטיקאים כדי להקל על השימוש בו בבעיות מתמטיות מרובות. לדוגמה, הקבוע π עשוי להיות מוגדר כיחס בין אורך היקף מעגל לקוטר שלו.

מצד שמאל מופיעה הקבוצה אליה משתייך המספר:

• $\mathbb {N}$ – מספר טבעי.
• $\mathbb {Q}$ – מספר רציונלי.
• $\mathbb {T}$ – מספר טרנסצנדנטי.
• $\mathbb {A}$ – מספר אלגברי.
• $\mathbb {Z}$ – מספר שלם.
• $\mathbb {C}$ – מספר מרוכב.

בימי קדם

שם	סמל	ייצוג עשרוני	נוסחא	שנה	קבוצה
1	1	1	אין	פרהיסטוריה	$\mathbb {N}$
2	2	2	$1+1$	פרהיסטוריה	$\mathbb {N}$
0.5	1/2	0.5	$1/2$	פרהיסטוריה	$\mathbb {Q}$
פאי	$\pi$	3.14159 26535 89793 23846	היחס בין היקף המעגל לקוטרו	1600–1900 לפנה"ס	$\mathbb {T}$
השורש הריבועי של 2 (קרוי גם קבוע פיתגורס)	${\sqrt {2}}$	1.41421 35623 73095 04880	השורש החיובי של $x^{2}=2$	1600–1800 לפנה"ס	$\mathbb {A}$
השורש הריבועי של 3 (קרוי גם קבוע תאודורוס)	${\sqrt {3}}$	1.73205 08075 68877 29352	השורש החיובי של $x^{2}=3$	465–398 לפנה"ס	$\mathbb {A}$
השורש הריבועי של 5	${\sqrt {5}}$	2.23606 79774 99789 69640	השורש החיובי של $x^{2}=5$		$\mathbb {A}$
יחס הזהב (הקרוי גם על שם האות המסמלת אותו, פי)	${\varphi }$	1.61803 39887 49894 84820	${\frac {1+{\sqrt {5}}}{2}}$	~300 לפנה"ס	$\mathbb {A}$
יחס הכסף	$\delta _{S}$	2.41421 35623 73095 04880	${\sqrt {2}}+1$	~300 לפנה"ס	$\mathbb {A}$
אפס	0	0	איבר האפס במשוואה: $x+0=x$	300–100 לפנה"ס	$\mathbb {Z}$
−1	−1	−1	$1-2$	200–300 לפנה"ס	$\mathbb {Z}$
השורש השלישי של 2	${\sqrt[{3}]{2}}$	1.25992 10498 94873 16476	השורש הממשי של $x^{3}=2$	46–120 לפנה"ס	$\mathbb {A}$
השורש השלישי של 3	${\sqrt[{3}]{3}}$	1.44224 95703 07408 38232	השורש הממשי של $x^{3}=3$		$\mathbb {A}$
השורש ה-12 של 2	${\sqrt[{12}]{2}}$	1.05946 30943 59295 26456	השורש הממשי של $x^{12}=2$		$\mathbb {A}$
יחס הסופר-זהב	$\psi$	1.46557 12318 76780 2665	${\frac {1+{\sqrt[{3}]{\frac {29+3{\sqrt {93}}}{2}}}+{\sqrt[{3}]{\frac {29-3{\sqrt {93}}}{2}}}}{3}}$		$\mathbb {A}$

בימי הביניים

שם	סמל	ייצוג עשרוני	נוסחא	שנה	קבוצה
היחידה המדומה	${i}$	0 + 1i	שני השורשים של $x^{2}=-1$	1501–1576	$\mathbb {C}$
קבוע ואליס	$W$	2.09455 14815 42326 59148	${\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}$	1616–1703	$\mathbb {A}$
מספר אוילר	${e}$	2.71828 18284 59045 23536	$\lim _{n\to \infty }\!\left(\!1\!+\!{\frac {1}{n}}\right)^{n}$	1618	$\mathbb {T}$
הלוגריתם הטבעי של 2	$\ln(2)$	0.69314 71805 59945 30941	$\sum _{n=1}^{\infty }{\frac {1}{n2^{n}}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+\cdots$	1619, 1668	$\mathbb {T}$
חלום סופומור 1	${I}_{1}$	0.78343 05107 12134 40705	$\int _{0}^{1}\!x^{x}\,dx=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}={\frac {1}{1^{1}}}-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-\cdots$	1697
חלום סופומור 2	${I}_{2}$	1.29128 59970 62663 54040	$\int _{0}^{1}\!{\frac {dx}{x^{x}}}=\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}={\frac {1}{1^{1}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+\cdots$	1697
קבוע למניסקטה	${\varpi }$	2.62205 75542 92119 81046	$\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {1}{4}}\right)^{2}}=4{\sqrt {\tfrac {2}{\pi }}}\left({\tfrac {1}{4}}!\right)^{2}$	1718 to 1798	$\mathbb {T}$
קבוע אוילר-מסקרוני	${\gamma }$	0.57721 56649 01532 86060	${\begin{aligned}&\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}=\sum _{n=1}^{\infty }\left({\frac {1}{n}}-\ln \left(1+{\frac {1}{n}}\right)\right)\\&=\int _{0}^{1}-\ln \left(\ln {\frac {1}{x}}\right)\,dx=-\Gamma '(1)=-\Psi (1)\end{aligned}}$	1735	$\mathbb {R} \setminus \mathbb {Q}$?
קבוע ארדש-בורוויין	${E}_{\,B}$	1.60669 51524 15291 76378	$\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {1}{2^{mn}}}=\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!\cdots$	1749	$\mathbb {R} \setminus \mathbb {Q}$
קבוע אומגה	$\Omega$	0.56714 32904 09783 87299	$\Omega =W(1)={\frac {1}{\pi }}\int _{0}^{\pi }\log \left(1+{\frac {\sin t}{t}}e^{t\cot t}\right)dt$Where W is the Lambert W function	1758,1783	$\mathbb {T}$
קבוע לפלס	${\lambda }$	0.66274 34193 49181 58097	${\frac {x\;e^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$	~1782	$\mathbb {T}$
קבוע גאוס	${G}$	0.83462 68416 74073 18628	${\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,\left({\tfrac {1}{4}}!\right)^{2}}{\pi ^{3}{2}}}={\frac {2}{\pi }}\int _{0}^{1}{\frac {dx}{\sqrt {1-x^{4}}}}$כאשר agm הוא הממוצע האריתמטי-גאומטרי	1799	$\mathbb {T}$

במאה ה-19

שם	סמל	ייצוג עשרוני	נוסחא	שנה	קבוצה
Second Hermite constant	$\gamma _{2}$	1.15470 05383 79251 52901	${\frac {2}{\sqrt {3}}}$	1822 to 1901	$\mathbb {A}$
Liouville's constant	$L$	0.11000 10000 00000 00000 0001	$\sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots$	Before 1844	$\mathbb {T}$
First continued fraction constant	$C_{1}$	0.69777 46579 64007 98201	${\tfrac {1}{1+{\tfrac {1}{2+{\tfrac {1}{3+{\tfrac {1}{4+{\tfrac {1}{5+\cdots }}}}}}}}}}$ ${\frac {I_{1}(2)}{I_{0}(2)}}$, where $I_{\alpha }(x)$ is the modified Bessel function	1855	$\mathbb {R} \setminus \mathbb {Q}$
Ramanujan's constant		262 53741 26407 68743 .99999 99999 99250 073	$e^{\pi {\sqrt {163}}}$	1859	$\mathbb {T}$
Glaisher–Kinkelin constant	$A$	1.28242 71291 00622 63687	$e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	1860
Catalan's constant	$G$	0.91596 55941 77219 01505	$\int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {dx\,dy}{1{+}x^{2}y^{2}}}=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }$	1864
Dottie number		0.73908 51332 15160 64165	Real root of $\cos x=x$	1865	$\mathbb {T}$
Meissel–Mertens constant	$M$	0.26149 72128 47642 78375	$\lim _{n\to \infty }\left(\sum _{p\leq n}{\frac {1}{p}}\ln \ln n\right)=\gamma +\sum _{p}\left(\ln \left(1-{\frac {1}{p}}\right)+{\frac {1}{p}}\right)$ where γ is the Euler–Mascheroni constant and p is prime	1866 & 1873
Universal parabolic constant	$P$	2.29558 71493 92638 07403	$\ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arsinh} (1)+{\sqrt {2}}$	Before 1891	$\mathbb {T}$
Cahen's constant	$C$	0.64341 05462 88338 02618	$\sum _{k=1}^{\infty }{\frac {(-1)^{k}}{s_{k}-1}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{6}}-{\frac {1}{42}}+{\frac {1}{1806}}{\,\pm \cdots }$ where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...	1891	$\mathbb {T}$

1900–1949

שם	סמל	ייצוג עשרוני	נוסחא	שנה	קבוצה
Gelfond's constant	$e^{\pi }$	23.14069 26327 79269 0057	$(-1)^{-i}=i^{-2i}=\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}=1+{\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2}}+{\frac {\pi ^{3}}{6}}+\cdots$	1900	$\mathbb {T}$
Gelfond–Schneider constant	$2^{\sqrt {2}}$	2.66514 41426 90225 18865		Before 1902	$\mathbb {T}$
Second Favard constant	$K_{2}$	1.23370 05501 36169 82735	${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots$	1902 to 1965	$\mathbb {T}$
Golden angle	$g$	2.39996 32297 28653 32223	${\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})$ or $180(3-{\sqrt {5}})=137.50776\ldots$ in degrees	1907	$\mathbb {T}$
Sierpiński's constant	$K$	2.58498 17595 79253 21706	${\begin{aligned}&\pi \left(2\gamma +\ln {\frac {4\pi ^{3}}{\Gamma ({\tfrac {1}{4}})^{4}}}\right)=\pi (2\gamma +4\ln \Gamma ({\tfrac {3}{4}})-\ln \pi )\\&=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)\end{aligned}}$	1907
Landau–Ramanujan constant	$K$	0.76422 36535 89220 66299	${\frac {1}{\sqrt {2}}}\prod _{{p\equiv 3{\text{ mod }}4} \atop p\;{\rm {prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}\!\!={\frac {\pi }{4}}\prod _{{p\equiv 1{\text{ mod }}4} \atop p\;{\rm {prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}$	1908
First Nielsen–Ramanujan constant	$a_{1}$	0.82246 70334 24113 21823	${\frac {{\zeta }(2)}{2}}={\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}\cdots$	1909	$\mathbb {T}$
Gieseking constant	$G$	1.01494 16064 09653 62502	${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$.	1912
Bernstein's constant	$\beta$	0.28016 94990 23869 13303	$\lim _{n\to \infty }2nE_{2n}(f)$, 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		1.83928 67552 14161 13255	${\textstyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {33}}}}+{\sqrt[{3}]{19-3{\sqrt {33}}}}}{3}}={\frac {1+4\cosh \left({\frac {1}{3}}\cosh ^{-1}\left(2+{\frac {3}{8}}\right)\right)}{3}}}$ Real root of $x^{3}-x^{2}-x-1=0$	1914 to 1963	$\mathbb {A}$
Brun's constant	$B_{2}$	1.90216 05831 04 תבנית:Refn	$\textstyle {\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+2}})}=({\frac {1}{3}}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}})+\cdots$ where the sum ranges over all primes p such that p + 2 is also a prime	1919
Twin primes constant	$C_{2}$	0.66016 18158 46869 57392	$\prod _{\textstyle {p\;{\rm {prime}} \atop p\geq 3}}\left(1-{\frac {1}{(p-1)^{2}}}\right)$	1922
Plastic number	$\rho$	1.32471 79572 44746 02596	${\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {\sqrt {69}}{18}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {\sqrt {69}}{18}}}}$ Real root of $x^{3}=x+1$	1924	$\mathbb {A}$
Bloch's constant	$B$	$0.4332\leq B\leq 0.4719$	The best known bounds are ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$	1925
Z score for the 97.5 percentile point	$z_{.975}$	1.95996 39845 40054 23552	${\sqrt {2}}\operatorname {erf} ^{-1}(0.95)$ where erf−1(x) is the inverse error function Real number $z$ such that ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$	1925
Landau's constant	$L$	$0.5<L\leq 0.54326$	The best known bounds are $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$	1929
Landau's third constant	$A$	$0.5<A\leq 0.7853$		1929
Prouhet–Thue–Morse constant	$\tau$	0.41245 40336 40107 59778	$\sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}={\frac {1}{4}}\left[2-\prod _{n=0}^{\infty }\left(1-{\frac {1}{2^{2^{n}}}}\right)\right]$ where ${t_{n}}$ is the nth term of the Thue–Morse sequence	1929	$\mathbb {T}$
Golomb–Dickman constant	$\lambda$	0.62432 99885 43550 87099	$\int _{0}^{1}e^{\mathrm {Li} (t)}dt=\int _{0}^{\infty }{\frac {\rho (t)}{t+2}}dt$ 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	$c$	0.98943 12738 31146 95174	$\lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)$	1930
Feller–Tornier constant	${\mathcal {C}}_{\mathrm {FT} }$	0.66131 70494 69622 33528	${{\frac {1}{2}}\prod _{p{\text{ prime}}}\left(1-{\frac {2}{p^{2}}}\right)+{\frac {1}{2}}}={\frac {3}{\pi ^{2}}}\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p^{2}-1}}\right)+{\frac {1}{2}}$	1932
Base 10 Champernowne constant	$C_{10}$	0.12345 67891 01112 13141	Defined by concatenating representations of successive integers: 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...	1933	$\mathbb {T}$
Salem constant	$\sigma _{10}$	1.17628 08182 59917 50654	Largest real root of $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$	1933	$\mathbb {A}$
Khinchin's constant	$K_{0}$	תבנית:Nobr	$\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\log _{2}(n)}$	1934
Lévy's constant (1)	$\beta$	1.18656 91104 15625 45282	${\frac {\pi ^{2}}{12\,\ln 2}}$	1935
Lévy's constant (2)	$e^{\beta }$	3.27582 29187 21811 15978	$e^{\pi ^{2}/(12\ln 2)}$	1936
Copeland–Erdős constant	${\mathcal {C}}_{CE}$	0.23571 11317 19232 93137	Defined by concatenating representations of successive prime numbers: 0.2 3 5 7 11 13 17 19 23 29 31 37 ...	1946	$\mathbb {R} \setminus \mathbb {Q}$
Mills' constant	$A$	1.30637 78838 63080 69046	Smallest positive real number A such that $\lfloor A^{3^{n}}\rfloor$ is prime for all positive integers n	1947
Gompertz constant	$\delta$	0.59634 73623 23194 07434	$\int _{0}^{\infty }\!\!{\frac {e^{-x}}{1+x}}\,dn=\!\!\int _{0}^{1}\!\!{\frac {dx}{1-\ln x}}={\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {2}{1+{\tfrac {2}{1+{\tfrac {3}{1+3{/\cdots }}}}}}}}}}}}}$	Before 1948

1950–1999

שם	סמל	ייצוג עשרוני	נוסחא	שנה	קבוצה
de Bruijn–Newman constant	$\Lambda$	$0\leq \Lambda \leq 0.2$	The number Λ where for where $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ has real zeros if and only if λ ≥ Λ. where $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$.	1950
Van der Pauw constant	${\frac {\pi }{\ln 2}}$	4.53236 01418 27193 80962		Before 1958	$\mathbb {R} \setminus \mathbb {Q}$
Magic angle	$\theta _{\mathrm {m} }$	0.95531 66181 245092 78163	$\arctan {\sqrt {2}}=\arccos {\tfrac {1}{\sqrt {3}}}\approx \textstyle {54.7356}^{\circ }$	Before 1959	$\mathbb {T}$
Artin's constant	$C_{\mathrm {Artin} }$	0.37395 58136 19202 28805	$\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p(p-1)}}\right)$	Before 1961
Porter's constant	$C$	1.46707 80794 33975 47289	${\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}$ where γ is the Euler–Mascheroni constant and ζ '(2) is the derivative of the Riemann zeta function evaluated at s = 2	1961
Lochs constant	$L$	0.97027 01143 92033 92574	${\frac {6\ln 2\ln 10}{\pi ^{2}}}$	1964
DeVicci's tesseract constant		1.00743 47568 84279 37609	The largest cube that can pass through in an 4D hypercube. Positive root of $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$	1966	$\mathbb {A}$
Lieb's square ice constant		1.53960 07178 39002 03869	$\left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}$	1967	$\mathbb {A}$
Niven's constant	$C$	1.70521 11401 05367 76428	$1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)$	1969
Stephens' constant		0.57595 99688 92945 43964	$\prod _{p{\text{ prime}}}\left(1-{\frac {p}{p^{3}-1}}\right)$	1969
Regular paperfolding sequence	$P$	0.85073 61882 01867 26036 תבנית:Refn	$\sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}$	1970	$\mathbb {T}$
Reciprocal Fibonacci constant	$\psi$	3.35988 56662 43177 55317	$\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ where Fn is the nth Fibonacci number	1974	$\mathbb {R} \setminus \mathbb {Q}$
Chvátal–Sankoff constant for the binary alphabet	$\gamma _{2}$	$0.788071\leq \gamma _{2}\leq 0.826280$	$\lim _{n\to \infty }{\frac {\operatorname {E} [\lambda _{n,2}]}{n}}$ where E[λn,2] is the expected longest common subsequence of two random length-n binary strings	1975
Feigenbaum constant δ	$\delta$	4.66920 16091 02990 67185 תבנית:Refn	$\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}$ where the sequence xn is given by $x_{n+1}=ax_{n}(1-x_{n})$	1975
Chaitin's constants	$\Omega$	In general they are uncomputable numbers. But one such number is 0.00787 49969 97812 3844	$\sum _{p\in P}2^{-|p|}$ p: Halted program תבנית:Abs: Size in bits of program p P: Domain of all programs that stop.	1975	$\mathbb {T}$
Robbins constant	$\Delta (3)$	0.66170 71822 67176 23515	${\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}$	1977	$\mathbb {T}$
Weierstrass constant		0.47494 93799 87920 65033	${\frac {2^{5/4}{\sqrt {\pi }}\,e^{\pi /8}}{\Gamma ({\frac {1}{4}})^{2}}}$	Before 1978	$\mathbb {T}$
Fransén–Robinson constant	$F$	2.80777 02420 28519 36522	$\int _{0}^{\infty }{\frac {dx}{\Gamma (x)}}=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	1978
Fractal dimension of the Cantor set	$\log _{3}2$	0.63092 97535 71457 43709	${\frac {\log 2}{\log 3}}$	Before 1979	$\mathbb {T}$
Feigenbaum constant α	$\alpha$	2.50290 78750 95892 82228 תבנית:Refn	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	$C_{2}$	0.19452 80494 65325 11361	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{n}}\right|\,dt-1$	1983	$\mathbb {T}$
Erdős–Tenenbaum–Ford constant	$\delta$	0.86071 33205 59342 06887	$1-{\frac {1+\log \log 2}{\log 2}}$	1984
Conway's constant	$\lambda$	1.30357 72690 34296 39125	Real root of the polynomial: ${\begin{smallmatrix}x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}$	1987	$\mathbb {A}$
Fractal dimension of the Apollonian packing of circles		1.30568 6729 ≈ by Thomas & Dhar 1.30568 8 ≈ by McMullen		1991
Hafner–Sarnak–McCurley constant	$\sigma$	0.35323 63718 54995 98454	$\prod _{p{\text{ prime}}}{\left(1-\left(1-\prod _{n\geq 1}\left(1-{\frac {1}{p^{n}}}\right)\right)^{2}\right)}\!$	1991
Hausdorff dimension of the Sierpinski triangle	$\log _{2}3$	1.58496 25007 21156 18145	${\frac {\log 3}{\log 2}}$	1993	$\mathbb {T}$
Backhouse's constant	$B$	1.45607 49485 82689 67139	$\lim _{k\to \infty }\left|{\frac {q_{k+1}}{q_{k}}}\right\vert \quad \scriptstyle {\text{where:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty }q_{k}x^{k}$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$where pk is the kth prime number	1995
Viswanath constant		1.13198 82487 943	$\lim _{n\to \infty }|f_{n}|^{\frac {1}{n}}$      where fn = fn−1 ± fn−2, where the signs + or − are chosen at random with equal probability 1/2	1997
Komornik–Loreti constant	$q$	1.78723 16501 82965 93301	Real number $q$ such that $1=\sum _{n=1}^{\infty }{\frac {t_{k}}{q^{k}}}$, or $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ where tk is the kth term of the Thue–Morse sequence	1998	$\mathbb {T}$
Embree–Trefethen constant	$\beta ^{\star }$	0.70258		1999
Heath-Brown–Moroz constant	$C$	0.00131 76411 54853 17810	$\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p}}\right)^{7}\left(1+{\frac {7p+1}{p^{2}}}\right)$	1999
MRB constant	$S$	0.18785 96424 62067 12024	$\sum _{n=1}^{\infty }(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots$	1999
Prime constant	$\rho$	0.41468 25098 51111 66024	$\sum _{p{\text{ prime}}}{\frac {1}{2^{p}}}={\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{32}}+\cdots$	1999	$\mathbb {R} \setminus \mathbb {Q}$
Somos' quadratic recurrence constant	$\sigma$	1.66168 79496 33594 12129	$\prod _{n=1}^{\infty }n^{{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots$	1999

2000 והלאה

שם	סמל	ייצוג עשרוני	נוסחא	שנה	קבוצה
Foias constant α	$F_{\alpha }$	1.18745 23511 26501 05459 תבנית:Refn	$x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ for }}n=1,2,3,\ldots$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 תבנית:Refn	$x^{x+1}=(x+1)^{x}$	2000	$\mathbb {T}$
DeVicci's tesseract constant	${f_{(3,4)}}$	1.00743 47568 84279 37609	The largest cube that can pass through in an 4D hypercube. Positive root of $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$	Before 2001	$\mathbb {A}$
Ramanujan nested radical	$R_{5}$	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	$\mathbb {A}$
Brun 4 constant = Σ inv.prime quadruplets	${B}_{\,4}$	0.87058 83799 75 תבנית:Refn	$\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
Hausdorff dimension, Sierpinski triangle	${\log _{2}3}$	1.58496 25007 21156 18145	${\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	$\mathbb {T}$
Heath-Brown–Moroz constant	${C_{_{HBM}}}$	0.00131 76411 54853 17810	${\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	$\mathbb {T}$?
Lebesgue constant	${C_{1}}$	0.98943 12738 31146 95174	$\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
2nd du Bois-Reymond constant	${C_{2}}$	0.19452 80494 65325 11361	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{n}}\right|\,dt-1$	Before 2003	$\mathbb {T}$
Logarithmic capacity of the unit disk		0.59017 02995 08048 11302	${\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}$	Before 2003	$\mathbb {T}$
Landau–Ramanujan constant	$K$	0.76422 36535 89220 66299	${\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	$\mathbb {T}$?
Stephens constant	$C_{S}$	0.57595 99688 92945 43964	$\prod _{n=1}^{\infty }\left(1-{\frac {p}{p^{3}-1}}\right)$	Before 2005	$\mathbb {T}$?
Taniguchi constant	$C_{T}$	0.67823 44919 17391 97803	$\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	$\mathbb {T}$?
Raabe's formula	${\zeta '(0)}$	0.91893 85332 04672 74178	$\int _{a}^{a+1}\log \Gamma (t)\,dt={\tfrac {1}{2}}\log 2\pi +a\log a-a,\quad a\geq 0$	Before 2011
Copeland–Erdős constant	${{\mathcal {C}}_{CE}}$	0.23571 11317 19232 93137	$\sum _{n=1}^{\infty }{\frac {p_{n}}{10^{n+\sum \limits _{k=1}^{n}\lfloor \log _{10}{p_{k}}\rfloor }}}$	Before 2012	$\mathbb {R} \setminus \mathbb {Q}$
Kepler–Bouwkamp constant	${\rho }$	0.11494 20448 53296 20070	$\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...$	Before 2013
Prouhet–Thue–Morse constant	$\tau$	0.41245 40336 40107 59778	$\sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}$    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	$\mathbb {T}$

ראו גם

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