Följande tabell innehåller en förteckning över konstanter och serier inom matematiken med följande kolumner:
| Värde | Namn | Symbol | LaTeX | Formel | Typ | OEIS | Fortsatt fraktion |
| 3.24697960371746706105000976800847962 | Silver, Tutte-Beraha konstant | ς {\displaystyle \varsigma }  | 2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 7 + 7 + 7 7 7 + 7 7 7 + ⋯ 3 3 3 3 1 + 7 + 7 7 7 7 + 7 7 7 + ⋯ 3 3 3 3 {\displaystyle 2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}} ![{\displaystyle 2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}}](https://www.alegsaonline.com/image/63c2ba5c39dd844946fe3ac7702fa5e6b6460472.svg) | 2+2 cos(2Pi/7) | T | A116425 | [3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...] |
| 1.09864196439415648573466891734359621 | Paris konstant | C P a {\displaystyle C_{Pa}}  | ∏ n = 2 ∞ 2 φ φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}}  | | I | A105415 | [1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...] |
| 2.74723827493230433305746518613420282 | Ramanujans inbäddade radikal R5 | R 5 {\displaystyle R_{5}}  | 5 + 5 + 5 + 5 - 5 + 5 + 5 + 5 + 5 - ⋯ = 2 + 5 + 15 - 6 5 2 {\displaystyle \scriptstyle {\sqrt {5+{\sqrt {5+{\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}}}  | (2+sqrt(5)+sqrt(15-6 sqrt(5)))/2 | I | | [2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...] |
| 2.23606797749978969640917366873127624 | Kvadratrot av 5, Gauss-summa | 5 {\displaystyle {\sqrt {5}}}  | ∀ n = 5 , ∑ k = 0 n - 1 e 2 k 2 π i n = 1 + e 2 π i 5 + e 8 π i 5 + e 18 π i 5 + e 32 π i 5 {\displaystyle \scriptstyle \scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}}}  | Sum[k=0 till 4]{e^(2k^2 pi i/5)} | I | A002163 | [2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...]
= [2;(4),...] |
| 3.62560990822190831193068515586767200 | Gamma(1/4) | Γ ( 1 4 ) {\displaystyle \Gamma ({\tfrac {1}{4}}})}  | 4 ( 1 4 ) ! = ( - 3 4 ) ! {\displaystyle 4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!}  | 4(1/4)! | T | A068466 | [3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...] |
| 0.18785964246206712024851793405427323 | MRB konstant, Marvin Ray Burns | C M R B {\displaystyle C_{_{MRB}}}  | ∑ n = 1 ∞ ( - 1 ) n ( n 1 / n - 1 ) = - 1 1 + 2 2 2 - 3 3 3 + 4 4 ... {\displaystyle \sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots } ![{\displaystyle \sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots }](https://www.alegsaonline.com/image/870bc7fa0415cfa4f3c3fb9253254c65e8e9d967.svg) | Sum[n=1 till ∞]{(-1)^n (n^(1/n)-1)} | T | A037077 | [0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...] |
| 0.11494204485329620070104015746959874 | Kepler-Bouwkamp-konstanten | ρ {\displaystyle {\rho }}  | ∏ n = 3 ∞ cos ( π n ) = cos ( π 3 ) cos ( π 4 ) cos ( π 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)\dots }  | prod[n=3 till ∞]{cos(pi/n)} | T | A085365 | [0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...] |
| 1.78107241799019798523650410310717954 | Exp(gamma)
G-Barnes-funktion | e γ {\displaystyle e^{\gamma }}  | ∏ n = 1 ∞ e 1 n 1 + 1 n = ∏ n = 0 ∞ ( ∏ k = 0 n ( k + 1 ) ( - 1 ) k + 1 ( n k ) ) 1 n + 1 = {\displaystyle \prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}}=}  ( 2 1 ) 1 / 2 ( 2 2 1 ⋅ 3 ) 1 / 3 ( 2 3 ⋅ 4 1 ⋅ 3 3 ) 1 / 4 ( 2 4 ⋅ 4 4 1 ⋅ 3 6 ⋅ 5 ) 1 / 5 ... {\displaystyle \textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}}{1\cdot 3^{6}\cdot 5}\right)^{1/5}\dots }  | Prod[n=1 till ∞]{e^(1/n)}/{1 + 1/n} | T | A073004 | [1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...] |
| 1.28242712910062263687534256886979172 | Glaisher-Kinkelin-konstant | A {\displaystyle {A}}  | e 1 12 - ζ ′ ( - 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)}}  | e^(1/2-zeta´{-1}) | T | A074962 | [1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...] |
| 7.38905609893065022723042746057500781 | Schwarzschilds koniska konstant | e 2 {\displaystyle e^{2}}  | ∑ n = 0 ∞ 2 n n n ! = 1 + 2 + 2 2 2 ! + 2 3 3 ! + 2 4 4 ! + 2 5 5 ! + ... {\displaystyle \sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots }  | Sum[n=0 till ∞]{2^n/n!} | T | A072334 | [7;2,1,1,1,3,18,5,1,1,1,6,30,8,1,1,1,9,42,11,1,...]
= [7,2,(1,1,1,n,4*n+6,n+2)], n = 3, 6, 9, etc. |
| 1.01494160640965362502120255427452028 | Gieseking konstant | G G i {\displaystyle {G_{Gi}}}  | 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)=}  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 \dots \right)} . | | T | A143298 | [1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...] |
| 2.62205755429211981046483958989111941 | Lemniscata konstant | ϖ {\displaystyle {\varpi }}  | π G = 4 2 π ( 1 4 ! ) 2 {\displaystyle \pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}}\,({\tfrac {1}{4}}}!)^{2}}}  | 4 sqrt(2/pi) (1/4!)^2 | T | A062539 | [2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...] |
| 0.83462684167407318628142973279904680 | Gauss-konstant | G {\displaystyle {G}}  | 1 a g m ( 1 , 2 ) = 4 2 ( 1 4 ! ) 2 π 3 / 2 A g m : A r i t h m e t i c - g e o m e t r i c m e a n {\displaystyle {\underset {Agm:\;Aritmetisk-geometrisk\;medel}{{\frac {1}{\mathrm {agm} (1,{\sqrt {2}}})}}={\frac {4{\sqrt {2}}}\,({\tfrac {1}{4}}!)^{2}}}{\pi ^{3/2}}}}}}  | (4 sqrt(2)(1/4!)^2)/pi^(3/2) | T | A014549 | [0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...] |
| 1.01734306198444913971451792979092052 | Zeta(6) | ζ ( 6 ) {\displaystyle \zeta (6)}  | π 6 945 = ∏ n = 1 ∞ 1 1 1 - p n - 6 p n : p r i m o = 1 1 1 - 2 - 6 ⋅ 1 1 1 - 3 - 6 ⋅ 1 1 - 5 - 6 . . . {\displaystyle {\frac {\pi ^{6}}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{{1-p_{n}}^{-6}}}}={\frac {1}{1{1{-}2^{-6}}}{\cdot }{\frac {1}{1{1{-}3^{-6}}}{\cdot }{\frac {1}{1{1{-}5^{-6}}}}...}  | Prod[n=1 till ∞] {1/(1-tippremiär(n)^-6)} | T | A013664 | [1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...] |
| 0,60792710185402662866327677925836583 | Constante de Hafner-Sarnak-McCurley | 1 ζ ( 2 ) {\displaystyle {\frac {1}{\zeta (2)}}}  | 6 π 2 = ∏ n = 0 ∞ ( 1 - 1 p n 2 ) p n : p r i m o = ( 1 - 1 2 2 2 ) ( 1 - 1 3 2 ) ( 1 - 1 5 2 ) ... {\displaystyle {\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\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)\dots }  | Prod{n=1 till ∞} (1-1/ithprime(n)^2) | T | A059956 | [0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...] |
| 1.11072073453959156175397024751517342 | Förhållandet mellan en kvadrat och omskrivna eller inskrivna cirklar. | π 2 2 2 {\displaystyle {\frac {\pi }{2{\sqrt {2}}}}}  | ∑ n = 1 ∞ ( - 1 ) ⌊ n - 1 2 ⌋ 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 - ... {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}}\rfloor }}{2n+1}}}={\frac {1}{1}{1}}}+{\frac {1}{3}}}-{\frac {1}{5}}}-{\frac {1}{7}}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots }  | sum[n=1 till ∞]{(-1)^(floor((n-1)/2))/(2n-1)} | T | A093954 | [1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...] |
| 2.80777024202851936522150118655777293 | Fransén-Robinson-konstanten | F {\displaystyle {F}}  | ∫ 0 ∞ 1 Γ ( x ) d x . = e + ∫ 0 ∞ e - x π 2 + ln 2 x d x {\displaystyle \int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx}  | N[int[0 till ∞] {1/Gamma(x)}] | T | A058655 | [2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...] |
| 1.64872127070012814684865078781416357 | Kvadratrot av talet e | e {\displaystyle {\sqrt {e}}}  | ∑ n = 0 ∞ 1 2 n n n ! = ∑ n = 0 ∞ 1 ( 2 n ) ! ! = 1 1 + 1 2 + 1 8 + 1 48 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}{1}}}+{\frac {1}{2}}}+{\frac {1}{8}}}+{\frac {1}{48}}+\cdots }  | sum[n=0 till ∞]{1/(2^n n!)} | T | A019774 | [1;1,1,1,1,1,5,1,1,1,9,1,1,1,13,1,1,1,17,1,1,1,1,21,1,1,1,...]
= [1;1,(1,1,4p+1)], p∈ℕ |
| i | Imaginärt tal | i {\displaystyle {i}}  | - 1 = ln ( - 1 ) π e i π = - 1 {\displaystyle {\sqrt {-1}}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1}  | sqrt(-1) | C | | |
| 262537412640768743.999999999999250073 | Hermite-Ramanujan-konstant | R {\displaystyle {R}}  | e π 163 {\displaystyle e^{\pi {\sqrt {163}}}}  | e^(π sqrt(163)) | T | A060295 | [262537412640768743;1,1333462407511,1,8,1,1,5,...] |
| 4.81047738096535165547303566670383313 | John konstant | γ {\\displaystyle \gamma }  | i i = i - i = i 1 i = ( i i i ) - 1 = e π 2 {\displaystyle {\sqrt[{i}]{i}}=i^{-i}=i^{\frac {1}{i}}}=(i^{{i})^{-1}=e^{\frac {\pi }{2}}}} ![{\displaystyle {\sqrt[{i}]{i}}=i^{-i}=i^{\frac {1}{i}}=(i^{i})^{-1}=e^{\frac {\pi }{2}}}](https://www.alegsaonline.com/image/904fff5ea95018fde18c45c94097a379edad291e.svg) | e^(π/2) | T | A042972 | [4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,...] |
| 4.53236014182719380962768294571666681 | Constante de Van der Pauw | α {\\displaystyle \alpha }  | π l n ( 2 ) = ∑ n = 0 ∞ 4 ( - 1 ) n 2 n + 1 ∑ n = 1 ∞ ( - 1 ) n + 1 n = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - ... 1 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ... {\displaystyle {\frac {\pi }{ln(2)}}}={\frac {\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}}{2n+1}}}{\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}}{n}}}}={\frac {{\frac {{4}{1}}}{-}{\frac {4}{3}}}{+}{\frac {4}{5}}}{-}{\frac {4}{7}}}{+}{\frac {4}{9}}}-\dots }{{\frac {1}{1}{1}}}}{-}{\frac {1}{2}}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}}{+}{\frac {1}{5}}-\dots }}}  | π/ln(2) | T | A163973 | [4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...] |
| 0.76159415595576488811945828260479359 | Hyperbolisk tangent (1) | t h 1 {\displaystyle th\,1}  | e - 1 e e + 1 e = e 2 - 1 e 2 + 1 {\displaystyle {\frac {e-{\frac {1}{e}}}{e+{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}}}  | (e-1/e)/(e+1/e) | T | A073744 | [0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...]
= [0;(2p+1)], p∈ℕ |
| 0.69777465796400798200679059255175260 | Fortsatt Fraktionskonstant | C C F {\displaystyle {C}_{CF}}}  | J 1 ( 2 ) J 0 ( 2 ) F u n k t i o n J k ( ) B e s s e l = ∑ n = 0 ∞ n n ! n ! n ! n ! ∑ n = 0 ∞ 1 n ! n ! n ! = 0 1 + 1 1 + 2 4 + 3 36 + 4 576 + ... 1 1 + 1 1 + 1 4 + 1 36 + 1 576 + ... {\displaystyle {\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}}{\\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {{\frac {0}{1}}}+{\frac {1}{1}}}+{\frac {2}{4}}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}{1}}}+{\frac {1}{1}{1}}}+{\frac {1}{1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}  | (summa {n=0 till inf} n/(n!n!)) /(summa {n=0 till inf} 1/(n!n!)) | | A052119 | [0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...]
= [0;(p+1)], p∈ℕ |
| 0.36787944117144232159552377016146086 | Omvänd Napierkonstant | 1 e {\displaystyle {\frac {\frac {1}{e}}}}  | ∑ n = 0 ∞ ( - 1 ) n n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! + ... {\displaystyle \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots }  | sum[n=2 till ∞]{(-1)^n/n!} | T | A068985 | [0;2,1,1,2,1,1,1,4,1,1,1,6,1,1,1,8,1,1,1,10,1,1,1,12,...]
= [0;2,1,(1,2p,1)], p∈ℕ |
| 2.71828182845904523536028747135266250 | Napier konstant | e {\displaystyle e}  | ∑ n = 0 ∞ 1 n ! = 1 0 ! + 1 1 + 1 2 ! + 1 3 ! + 1 4 ! + 1 5 ! + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}{1}}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots }  | Sum[n=0 till ∞]{1/n!} | T | A001113 | [2;1,2,1,1,4,1,1,1,6,1,1,8,1,1,1,10,1,1,1,12,1,...]
= [2;(1,2p,1)], p∈ℕ |
| 0.49801566811835604271369111746219809
- 0.15494982830181068512495513048388 i | Faktorn för i | i ! {\displaystyle i\,!}  | Γ ( 1 + i ) = i Γ ( i ) {\displaystyle \Gamma (1+i)=i\,\Gamma (i)}  | Gamma(1+i) | C | A212877
A212878 | [0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...]
- [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i |
| 0.43828293672703211162697516355126482
+ 0.36059247187138548595294052690600 i | Oändlig
Tetration av i | ∞ i {\displaystyle {}^{\infty }i}  | lim n → ∞ n i = lim n → ∞ i i ⋅ ⋅ i ⏟ n {\displaystyle \lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}}  | i^i^i^i^... | C | A077589
A077590 | [0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...]
+ [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i |
| 0.56755516330695782538461314419245334 | Modul av
oändlig
Tetration av i | | ∞ i | {\displaystyle |{}^{\infty }i|}  | lim n → ∞ | n i | = | lim n → ∞ i ⋅ ⋅ ⋅ i ⏟ n | {\displaystyle \lim _{n\to \infty }\left|{}^{n}i\right|=\left|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right|}  | Mod(i^i^i^i^...) | | A212479 | [0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...] |
| 0.26149721284764278375542683860869585 | Meissel-Mertens konstant | M {\displaystyle M}  | lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) {\displaystyle \lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}}-\ln(\ln(n))\right)} ..... p: primtal | | | A077761 | [0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...] |
| 1.9287800... | Wright-konstant | ω {\displaystyle \omega }  | ⌊ 2 2 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{2^{2^{\cdot ^{\cdot ^{2^{{\omega }}}}}}\right\rfloor } = primos: {\\displaystyle \quad }  ⌊ 2 ω ⌋ {\displaystyle \left\lfloor 2^{\omega }\right\rfloor } =3, ⌊ 2 2 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{{omega }}\right\rfloor } =13, ⌊ 2 2 2 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{2^{2^{\omega }}}\right\rfloor } =16381, ... {\displaystyle \dots }  | | | A086238 | [1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3] |
| 0.37395581361920228805472805434641641 | Artin konstant | C A r t i n {\displaystyle C_{Artin}}  | ∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)} ...... pn : primo | | T | A005596 | [0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...] |
| 4.66920160910299067185320382046620161 | Feigenbaumkonstanten δ | δ {\ {\displaystyle {\delta }}  | lim n → ∞ x n + 1 - x n x n + 2 - x n + 1 x ∈ ( 3 , 8284 ; 3 , 8495 ) {\displaystyle \lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)}  x n + 1 = a x n ( 1 - x n ) o x n + 1 = a sin ( x n ) {\displaystyle \scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {o}\quad x_{n+1}=\,a\sin(x_{n})}  | | T | A006890 | [4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...] |
| 2.50290787509589282228390287321821578 | Feigenbaumkonstanten α | α {\\displaystyle \alpha } | lim n → ∞ d n d n d n + 1 {\displaystyle \lim _{n\to \infty }{\frac {d_{n}}}{d_{n+1}}}}  | | T | A006891 | [2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...] |
| 5.97798681217834912266905331933922774 | Hexagonal Madelung Constant 2 | H 2 ( 2 ) {\displaystyle H_{2}(2)}  | π ln ( 3 ) 3 {\displaystyle \pi \ln(3){\sqrt {3}}}  | Pi Log[3]Sqrt[3] | T | A086055 | [5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...] |
| 0.96894614625936938048363484584691860 | Beta(3) | β ( 3 ) {\displaystyle \beta (3)}  | π 3 32 = ∑ n = 1 ∞ - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 3 + 1 5 3 - 1 7 3 + ... {\displaystyle {\frac {\pi ^{3}}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}}{(-1+2n)^{3}}}}={\frac {1}{1^{3}}}}{-}{\frac {1}{3^{3}}}}{+}{\frac {1}{5^{3}}}}{-}{\frac {1}{7^{3}}}{+}\dots }  | Sum[n=1 till ∞]{(-1)^(n+1)/(-1+2n)^3} | T | A153071 | [0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...] |
| 1.902160583104 | Brun konstant2 = Σ omvända tvillingprimer | B 2 {\displaystyle B_{\,2}}  | ∑ ( 1 p + 1 p + 2 ) p , p + 2 : p r i m o s = ( 1 3 + 1 5 ) + ( 1 5 + 1 7 ) + ( 1 11 + 1 13 ) + ... {\displaystyle \textstyle \sum {\underset {p,\,p+2:\,{primos}}{({\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}})+\dots }  | | | A065421 | [1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2] |
| 0.870588379975 | Brunkonstanten4 = Σ omvänt av tvillingprimärvärdet | B 4 {\displaystyle B_{\,4}}  | ( 1 5 + 1 7 + 1 11 + 1 13 ) p , p + 2 , p + 4 , p + 6 : p r i m e s + ( 1 11 + 1 13 + 1 17 + 1 19 ) + ... {\displaystyle {\underset {p,\,p+2,\,p+4,\,\,p+6:\,{primes}}{\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 }  | | | A213007 | [0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] |
| 22.4591577183610454734271522045437350 | pi^e | π e {\displaystyle \pi ^{e}}  | π e {\displaystyle \pi ^{e}} | pi^e | | A059850 | [22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...] |
| 3.14159265358979323846264338327950288 | Pi, Archimedes konstant | π {\\displaystyle \pi }  | lim n → ∞ 2 n 2 2 - 2 + 2 + ⋯ + 2 ⏟ n {\displaystyle \lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}}  | Sum[n=0 till ∞]{(-1)^n 4/(2n+1)} | T | A000796 | [3;7,15,1,292,1,1,1,2,1,3,1,14,...] |
| 0.06598803584531253707679018759684642 | | e - e {\displaystyle e^{-e}}  | e - e {\displaystyle e^{-e}} ... Nedre gräns för Tetration | | T | A073230 | [0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...] |
| 0.20787957635076190854695561983497877 | i^i | i i i {\displaystyle i^{i}}  | e - π 2 {\displaystyle e^{\frac {-\pi }{2}}}  | e^(-pi/2) | T | A049006 | [0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...] |
| 0.28016949902386913303643649123067200 | Bernsteins konstant | β {\\displaystyle \beta }  | 1 2 π {\displaystyle {\frac {1}{2{\sqrt {\pi }}}}}  | | T | A073001 | [0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…] |
| 0.28878809508660242127889972192923078 | Flajolet och Richmond | Q {\displaystyle Q}  | ∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 2 1 ) ( 1 - 1 2 2 2 ) ( 1 - 1 2 3 ) ... {\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}}\right)\left(1{-}{\frac {1}{2^{2}}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)\dots }  | prod[n=1 till ∞]{1-1/2^n} | | A048651 | |
| 0.31830988618379067153776752674502872 | Invers av Pi, Ramanujan | 1 π {\displaystyle {\frac {\frac {1}{\pi }}}  | 2 2 2 9801 ∑ n = 0 ∞ ( 4 n ) ! ( 1103 + 26390 n ) ( n ! ) 4 396 4 n {\displaystyle {\frac {\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}}  | | T | A049541 | [0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...] |
| 0.47494937998792065033250463632798297 | Weierstraß konstant | W W W E {\displaystyle W_{_{WE}}}  | e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {\displaystyle {\frac {e^{\frac {\pi }{8}}}{\sqrt {\pi }}}{4*2^{3/4}{({\frac {1}{4}}}!)^{2}}}}}  | (E^(Pi/8) Sqrt[Pi])/(4 2^(3/4) (1/4)!^2) | T | A094692 | [0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,...] |
| 0.56714329040978387299996866221035555 | Omega-konstant | Ω {\displaystyle \Omega }  | W ( 1 ) = ∑ n = 1 ∞ ( - n ) n - 1 n ! = 1 - 1 + 3 2 - 8 3 + 125 24 - ... {\displaystyle W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}}{n!}}=1{-}1{+}{\frac {3}{2}}}{-}{\frac {8}{3}}}}{+}{\frac {125}{24}}-\dots }  | sum[n=1 till ∞]{(-n)^(n-1)/n!} | T | A030178 | [0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,...] |
| 0.57721566490153286060651209008240243 | Eulers tal | γ {\\displaystyle \gamma } | - ψ ( 1 ) = ∑ n = 1 ∞ ∑ k = 0 ∞ ( - 1 ) k 2 n + k {\displaystyle -\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}}}  | sum[n=1 till ∞]|sum[k=0 till ∞]{((-1)^k)/(2^n+k)} | ? | A001620 | [0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,...] |
| 0.60459978807807261686469275254738524 | Dirichlet-serien | π 3 3 3 {\displaystyle {\frac {\pi }{3{\sqrt {3}}}}}  | ∑ n = 1 ∞ 1 n ( 2 n n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}}+{\frac {1}{4}}}-{\frac {1}{5}}}+{\frac {1}{7}}}-{\frac {1}{8}}}+\cdots }  | Sum[1/(n Binomial[2 n, n]), {n, 1, ∞}] | T | A073010 | [0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,...] |
| 0.63661977236758134307553505349005745 | 2/Pi, François Viète | 2 π π {\displaystyle {\frac {2}{\pi }}}  | 2 2 2 ⋅ 2 + 2 2 2 ⋅ 2 + 2 + 2 + 2 2 ⋯ {\displaystyle {\frac {\sqrt {2}}{2}}}\cdot {\frac {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots }  | | T | A060294 | [0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...] |
| 0.66016181584686957392781211001455577 | Twin prime konstant | C 2 {\displaystyle C_{2}}  | ∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {\displaystyle \prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}}  | prod[p=3 till ∞]{p(p-2)/(p-1)^2 | | A005597 | [0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...] |
| 0.66274341934918158097474209710925290 | Laplace Gränskonstant | λ {\\displaystyle \lambda }  | | | | A033259 | [0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...] |
| 0.69314718055994530941723212145817657 | Logaritm de 2 | L n ( 2 ) {\displaystyle Ln(2)}  | ∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}}{n}}={\frac {1}{1}{1}}}-{\frac {1}{2}}}+{\frac {1}{3}}-{\frac {1}{4}}}+{\frac {1}{5}}-\cdots }  | Sum[n=1 till ∞]{(-1)^(n+1)/n} | T | A002162 | [0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...] |
| 0.78343051071213440705926438652697546 | Sophomore's Dream1 J.Bernoulli | I 1 {\displaystyle I_{1}}  | ∑ n = 1 ∞ ( - 1 ) n + 1 n n n = 1 - 1 2 2 2 + 1 3 3 3 - 1 4 4 4 + 1 5 5 + ... {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}}+{\frac {1}{3^{3}}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots }  | Sum[ -(-1)^n /n^n] | T | A083648 | [0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,...] |
| 0.78539816339744830961566084581987572 | Dirichlet beta(1) | β ( 1 ) {\displaystyle \beta (1)}  | π 4 = ∑ n = 0 ∞ ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - ⋯ {\displaystyle {\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}}{2n+1}}}={\frac {1}{1}{1}}}}-{\frac {1}{3}}}+{\frac {1}{5}}}-{\frac {1}{7}}}+{\frac {1}{9}}-\cdots }  | Sum[n=0 till ∞]{(-1)^n/(2n+1)} | T | A003881 | [0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,...] |
| 0.82246703342411321823620758332301259 | Resande försäljare Nielsen-Ramanujan | ζ ( 2 ) 2 {\displaystyle {\frac {\zeta (2)}{2}}}  | π 2 12 = ∑ n = 1 ∞ ( - 1 ) n + 1 n 2 = 1 1 2 - 1 2 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\displaystyle {\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}}}-\dots }  | Sum[n=1 till ∞]{((-1)^(k+1))/n^2} | T | A072691 | [0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,...] |
| 0.91596559417721901505460351493238411 | Katalansk konstant | C {\displaystyle C}  | ∑ n = 0 ∞ ( - 1 ) n ( 2 n + 1 ) 2 = 1 1 2 - 1 3 2 + 1 5 2 - 1 7 2 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {(-1)^{n}}}{(2n+1)^{2}}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}}+{\frac {1}{5^{2}}}}-{\frac {1}{7^{2}}}+\cdots }  | Sum[n=0 till ∞]{(-1)^n/(2n+1)^2} | I | A006752 | [0;1,10,1,8,1,88,4,1,1,7,22,1,2,...] |
| 1.05946309435929526456182529494634170 | Förhållandet mellan avståndet mellan halvtonerna | 2 12 {\displaystyle {\sqrt[{12}]{2}}}} ![{\displaystyle {\sqrt[{12}]{2}}}](https://www.alegsaonline.com/image/bc835f27425fb3140e1f75a5faa35b1e8b9efc35.svg) | 2 12 {\displaystyle {\sqrt[{12}]{2}}}} | 2^(1/12) | I | A010774 | [1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...] |
| 1,.08232323371113819151600369654116790 | Zeta(04) | ζ 4 {\displaystyle \zeta {4}}  | π 4 90 = ∑ n = 1 ∞ 1 n 4 = 1 1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 + 1 4 4 + 1 5 4 + ... {\displaystyle {\frac {\pi ^{4}}}{90}}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}}={\frac {1}{1^{4}}}}+{\frac {1}{2^{4}}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}}+\dots }  | Sum[n=1 till ∞]{1/n^4} | T | A013662 | [1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,...] |
| 1.1319882487943 ... | Viswanaths Arkiverad 2013-04-13 vid Wayback Machine konstant | C V i {\displaystyle C_{Vi}}  | lim n → ∞ | a n | 1 n {\displaystyle \lim _{n\to \infty }|a_{n}|^{\frac {1}{n}}}}  | | | A078416 | [1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...] |
| 1.20205690315959428539973816151144999 | Konstant apérium | ζ ( 3 ) {\displaystyle \zeta (3)}  | ∑ 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 \,\!}  | Sum[n=1 till ∞]{1/n^3} | I | A010774 | [1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,...] |
| 1.22541670246517764512909830336289053 | Gamma(3/4) | Γ ( 3 4 ) {\displaystyle \Gamma ({\tfrac {3}{4}})}  | ( - 1 + 3 4 ) ! {\displaystyle \left(-1+{\frac {3}{4}}\right)!}  | (-1+3/4)! | T | A068465 | [1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,...] |
| 1.23370055013616982735431137498451889 | Favardkonstant | 3 4 ζ ( 2 ) {\displaystyle {\tfrac {3}{4}}}\zeta (2)}  | π 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}}}+\dots }  | sum[n=1 till ∞]{1/((2n-1)^2)} | T | A111003 | [1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...] |
| 1.25992104989487316476721060727822835 | Kubikrot av 2, konstant Delian | 2 3 {\displaystyle {\sqrt[{3}]{2}}}} ![{\displaystyle {\sqrt[{3}]{2}}}](https://www.alegsaonline.com/image/9ca071ab504481c2bb76081aacb03f5519930710.svg) | 2 3 {\displaystyle {\sqrt[{3}]{2}}}} | 2^(1/3) | I | A002580 | [1;3,1,5,1,1,4,1,1,8,1,14,1,10,...] |
| 1.29128599706266354040728259059560054 | Sophomore's Dream2 J.Bernoulli | I 2 {\displaystyle I_{2}}  | ∑ n = 1 ∞ 1 n n n = 1 + 1 2 2 + 1 3 3 + 1 4 4 4 + 1 5 5 + 1 6 6 + ... {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{n}}}}=1+{\frac {1}{2^{2}}}}+{\frac {1}{3^{3}}}}+{\frac {1}{4^{4}}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}}+\dots }  | Sum[1/(n^n]), {n, 1, ∞}] | | A073009 | [1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,...] |
| 1.32471795724474602596090885447809734 | Plastnummer | ρ {\displaystyle \rho }  | 1 + 1 + 1 + 1 + 1 + ⋯ 3 3 3 3 3 3 {\displaystyle {\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+\cdots }}}}}}}}} ![{\displaystyle {\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+\cdots }}}}}}}}}](https://www.alegsaonline.com/image/fe5c1cba04372927a214a2ce1b1d6b213bb12ee3.svg) | | I | A060006 | [1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...] |
| 1.41421356237309504880168872420969808 | Kvadratroten av 2, Pythagoras konstant | 2 {\displaystyle {\sqrt {2}}}}  | ∏ n = 1 ∞ 1 + ( - 1 ) n + 1 2 n - 1 = ( 1 + 1 1 1 ) ( 1 - 1 3 ) ( 1 + 1 5 ) . . . {\displaystyle \prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}}{2n-1}}}=\left(1{+}{\frac {1}{1}}}\right)\left(1{-}{\frac {1}{3}}}\right)\left(1{+}{\frac {1}{5}}\right)...}  | prod[n=1 till ∞]{1+(-1)^(n+1)/(2n-1)} | I | A002193 | [1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]
= [1;(2),...] |
| 1.44466786100976613365833910859643022 | Steiner-tal | e 1 e {\displaystyle e^{\frac {1}{e}}}}  | e 1 / e {\displaystyle e^{1/e}}  ... Övre gräns för tetration | | | A073229 | [1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...] |
| 1.53960071783900203869106341467188655 | Lieb's Square Ice konstant | W 2 D {\displaystyle W_{2D}}  | lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 {\displaystyle \lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}}\right)^{\frac {3}{2}}}}  | (4/3)^(3/2) | I | A118273 | [1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...] |
| 1.57079632679489661923132169163975144 | Wallis-produkten | π / 2 {\displaystyle \pi /2}  | ∏ n = 1 ∞ ( 4 n 2 4 n 2 - 1 ) = 2 1 ⋅ 2 3 ⋅ 4 3 ⋅ 4 5 ⋅ 6 5 ⋅ 6 7 ⋅ 8 7 ⋅ 8 9 ⋯ {\displaystyle \prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}}\right)={\frac {2}{1}}}\cdot {\frac {2}{3}}}\cdot {\frac {4}{3}}}\cdot {\frac {4}{5}}}\cdot {\frac {6}{5}}}\cdot {\frac {6}{7}}}\cdot {\frac {8}{7}}}\cdot {\frac {8}{9}}\cdots }  | | T | A019669 | [1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1...] |
| 1.60669515241529176378330152319092458 | Erdős-Borwein-konstant | E B {\displaystyle E_{\,B}}  | ∑ n = 1 ∞ 1 2 n - 1 = 1 1 1 + 1 3 + 1 7 + 1 15 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}{1}}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!}  | sum[n=1 till ∞]{1/(2^n-1)} | I | A065442 | [1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...] |
| 1.61803398874989484820458633436563812 | Phi, gyllene snittet | φ {\\displaystyle \varphi }  | 1 + 5 2 = 1 + 1 + 1 + 1 + 1 + ⋯ {\displaystyle {\frac {\frac {1+{{\sqrt {5}}}}{2}}}={\sqrt {1+{{\sqrt {1+{\sqrt {1+{{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}}  | (1+5^(1/2))/2 | I | A001622 | [0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...]
= [0;(1),...] |
| 1.64493406684822643647241516664602519 | Zeta(2) | ζ ( 2 ) {\displaystyle \zeta (\,2)}  | π 2 6 = ∑ n = 1 ∞ 1 n 2 = 1 1 1 2 + 1 2 2 2 + 1 3 2 + 1 4 2 + ⋯ {\displaystyle {\frac {\pi ^{2}}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots }  | Sum[n=1 till ∞]{1/n^2} | T | A013661 | [1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...] |
| 1.66168794963359412129581892274995074 | Somos kvadratiska återkomstkonstant | σ {\\displaystyle \sigma }  | 1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {\sqrt {\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots }  | | T | A065481 | [1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...] |
| 1.73205080756887729352744634150587237 | Theodorus konstant | 3 {\displaystyle {\sqrt {3}}}  | 3 {\displaystyle {\sqrt {3}}} | 3^(1/2) | I | A002194 | [1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...]
= [1;(1,2),...] |
| 1.75793275661800453270881963821813852 | Kasner-nummer | R {\displaystyle R}  | 1 + 2 + 3 + 4 + ⋯ {\displaystyle {\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}}  | | | A072449 | [1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...] |
| 1.77245385090551602729816748334114518 | Carlson-Levin konstant | Γ ( 1 2 ) {\displaystyle \Gamma ({\tfrac {1}{2}})}  | π = ( - 1 2 ) ! {\displaystyle {\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!}  | sqrt (pi) | T | A002161 | [1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...] |
| 2.29558714939263807403429804918949038 | Universell parabolisk konstant | P 2 {\displaystyle P_{\,2}}  | ln ( 1 + 2 ) + 2 {\displaystyle \ln(1+{\sqrt {2}})+{\sqrt {2}}}}  | ln(1+sqrt 2)+sqrt 2 | T | A103710 | [2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,...] |
| 2.30277563773199464655961063373524797 | Brons nummer | σ R r {\displaystyle \sigma _{\,Rr}}  | 3 + 13 2 = 1 + 3 + 3 + 3 + 3 + 3 + ⋯ {\displaystyle {\frac {3+{\sqrt {13}}}}{2}}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}}  | (3+sqrt 13)/2 | I | A098316 | [3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...]
= [3;(3),...] |
| 2.37313822083125090564344595189447424 | Lévy-konstant2 | 2 ln γ {\displaystyle 2\,\ln \,\gamma }  | π 2 6 ln ( 2 ) {\displaystyle {\frac {\pi ^{2}}}{6\ln(2)}}}  | Pi^(2)/(6*ln(2)) | T | A174606 | [2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...] |
| 2.50662827463100050241576528481104525 | kvadratroten av 2 pi | 2 π {\displaystyle {\sqrt {2\pi }}}  | 2 π = lim n → ∞ n ! e n n n n n n {\displaystyle {\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}}  | sqrt (2*pi) | T | A019727 | [2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...] |
| 2.66514414269022518865029724987313985 | Gelfond-Schneider-konstanten | G G G S {\displaystyle G_{_{\,GS}}}  | 2 2 2 {\displaystyle 2^{\sqrt {2}}}}  | 2^sqrt{2} | T | A007507 | [2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...] |
| 2.68545200106530644530971483548179569 | Khintchin konstant | K 0 {\displaystyle K_{\,0}}  | ∏ n = 1 ∞ [ 1 + 1 n ( n + 2 ) ] ln n / ln 2 {\displaystyle \prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}}} ![{\displaystyle \prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}}](https://www.alegsaonline.com/image/cbfef25fcd2817842f1c50956dc798248c418be6.svg) | prod[n=1 till ∞]{(1+1/(n(n+2)))^((ln(n)/ln(2))} | ? | A002210 | [2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...] |
| 3.27582291872181115978768188245384386 | Khinchin-Lévy-konstant | γ {\\displaystyle \gamma } | e π 2 / ( 12 ln 2 ) {\displaystyle e^{\pi ^{2}/(12\ln 2)}}  | e^(\pi^2/(12 ln(2)) | | A086702 | [3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...] |
| 3.35988566624317755317201130291892717 | Reciprok Fibonacci-konstant | Ψ {\displaystyle \Psi }  | ∑ n = 1 ∞ 1 F n = 1 1 1 + 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}{1}}}+{\frac {1}{1}{1}}}+{\frac {1}{2}}}+{\frac {1}{3}}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots }  | | | A079586 | [3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...] |
| 4.13273135412249293846939188429985264 | Rot av 2 e pi | 2 e π {\displaystyle {\sqrt {2e\pi }}}  | 2 e π {\displaystyle {\sqrt {2e\pi }}} | sqrt(2e pi) | T | A019633 | [4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...] |
| 6.58088599101792097085154240388648649 | Froda konstant | 2 e {\displaystyle 2^{\,e}}  | 2 e {\displaystyle 2^{e}}  | 2^e | | | [6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...] |
| 9.86960440108935861883449099987615114 | Pi i kvadrat | π 2 {\displaystyle \pi ^{2}}  | 6 ∑ n = 1 ∞ 1 n 2 = 6 1 2 + 6 2 2 2 + 6 3 2 + 6 4 2 + ⋯ {\displaystyle 6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots }  | 6 Sum[n=1 till ∞]{1/n^2} | T | A002388 | [9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,...] |
| 23.1406926327792690057290863679485474 | Gelfond konstant | e π {\displaystyle e^{\pi }}  | ∑ n = 0 ∞ π n n n ! = π 1 1 1 + π 2 2 2 ! + π 3 3 ! + π 4 4 ! + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}}{1}}}+{\frac {\pi ^{2}}}{2!}}+{\frac {\pi ^{3}}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots }  | Sum[n=0 till ∞]{(pi^n)/n!} | T | A039661 | [23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...] |
