Mathematische Konstante

Eine mathematische Konstante ist eine Zahl, die für Berechnungen eine besondere Bedeutung hat. Zum Beispiel bedeutet die Konstante π (ausgesprochen "Kuchen") das Verhältnis des Umfangs eines Kreises zu seinem Durchmesser. Dieser Wert ist für jeden Kreis immer derselbe. Eine mathematische Konstante ist oft eine reale, nicht ganzzahlige Zahl von Interesse.

Im Gegensatz zu physikalischen Konstanten stammen mathematische Konstanten nicht aus physikalischen Messungen.

Wichtige mathematische Konstanten

Die folgende Tabelle enthält einige wichtige mathematische Konstanten:

Name	Symbol	Wert	Bedeutung
Pi, die Konstante des Archimedes oder die Ludoph-Zahl	π	≈3.141592653589793	Eine transzendente Zahl, die das Verhältnis der Länge des Umfangs eines Kreises zu seinem Durchmesser angibt. Sie ist auch die Fläche des Einheitskreises.
E, die Napier-Konstante	e	≈2.718281828459045	Eine transzendente Zahl, die die Basis der natürlichen Logarithmen ist, manchmal auch als "natürliche Zahl" bezeichnet.
Goldener Schnitt	φ	5 + 1 2 ≈ 1.618 {\displaystyle {\frac {{{\sqrt {5}}+1}{2}}\ca. 1.618} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	Es ist der Wert eines größeren Wertes geteilt durch einen kleineren Wert, wenn dieser gleich dem Wert der Summe der Werte geteilt durch den größeren Wert ist.
Quadratwurzel aus 2, Pythagoras-Konstante	2 {\displaystyle {\sqrt {2}}} ${\sqrt {2}}$	≈ 1.414 {\Anzeigestil \ca. 1.414} $\approx 1.414$	Eine irrationale Zahl, die die Länge der Diagonale eines Quadrats mit Seiten der Länge 1 ist. Diese Zahl kann nicht als Bruch geschrieben werden.

Konstanten und Reihen

Die folgende Tabelle enthält eine Liste von Konstanten und Reihen in der Mathematik mit den folgenden Spalten:

Wert: Numerischer Wert der Konstante.
LaTeX: Formel oder Serie im TeX-Format.
Formel: Zur Verwendung in Programmen wie Mathematica oder Wolfram Alpha.
OEIS: Link zur On-Line Encyclopedia of Integer Sequences (OEIS), wo die Konstanten mit weiteren Details verfügbar sind.
Fortsetzung der Fraktion: In der einfachen Form [zur Ganzzahl; frac1, frac2, frac3, ...] (in Klammern, falls periodisch)
Art:

R - Rationale Zahl
I - Irrationale Zahl
T - Transzendente Zahl
C - Komplexe Zahl

Beachten Sie, dass die Liste entsprechend geordnet werden kann, indem Sie auf den Titel der Kopfzeile oben in der Tabelle klicken.

Wert	Name	Symbol	LaTeX	Formel	Geben Sie ein.	OEIS	Fortsetzung der Fraktion
3.24697960371746706105000976800847962	Silber, Tutte-Beraha-Konstante	ς {\displaystyle \varsigma } $\varsigma$	2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 2 + 7 + 7 7 + 7 7 + 7 7 + ⋯ 3 3 3 3 1 + 7 + 7 7 + 7 7 + 7 7 + ⋯ 3 3 3 {\darstellungsstil 2+2\cos(2\pi /7)=\textstil 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 }}}}}}}}} $2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}$	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	Pariser Konstante	C P a {\Anzeigestil C_{Pa}} $C_{Pa}$	∏ n = 2 ∞ 2 ∞ 2 φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}}\;,\varphi ={Fi}} $\prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}$		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	Ramanujan verschachtelter Radikaler _R5	R 5 {\Anzeigestil R_{5}} $R_{5}$	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-\cdots }}}}}}}}}}}}}}\;=\Text-Stil {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}} $\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(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	Quadratwurzel aus 5, Gauß-Summe	5 {\ansichtsstil {\sqrt {5}}} ${\sqrt {5}}$	∀ n = 5 , ∑ k = 0 n - 1 und 2 k 2 π i n = 1 + und 2 π i 5 + und 8 π i 5 + und 18 π i 5 + und 32 π i 5 {\displaystyle \scriptstyle \forall \,n=5,\darstellungsstil \sum _{k=0} {\n-1}e{\frac {\2k}{2}{1+e{\frac {\2k}{5}+e{8}{5}+e{\frac {\i1}{1+e}. $\scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	Summe[k=0 bis 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}}})} $\Gamma ({\tfrac {1}{4}})$	4 ( 1 4 ) ! = ( − 3 4 ) ! {\Anzeigestil 4\links({\frac {1}{4}}\rechts)!=\links(-{\frac {3}{4}}\rechts)! } $4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	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 {\Anzeigestil C_{_{_{MRB}}} $C_{_{MRB}}$	∑ n = 1 ∞ ( - 1 ) n ( n 1 / n - 1 ) = - 1 1 1 + 2 2 - 3 3 + 4 4 ... {\darstellungsstil \sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\Punkte } $\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots$	Summe[n=1 bis ∞]{(-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-Konstante	ρ {\rho {\rho}} ${\rho }$	∏ n = 3 ∞ cos ( π n ) = cos ( π 3 ) cos ( π 4 ) cos ( π 5 ) ... {\Anzeigestil \prod _{n=3}^{\infty }\cos \left({\frac {\pi {n}}\right)=\cos {\frac {\pi }3}\right)\cos \left({\frac {\pi }{4}\right)\cos \left({\frac {\pi }{5}\right)\dots } $\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)\dots$	prod[n=3 bis ∞]{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 }} $e^{\gamma }$	∏ n = 1 ∞ e 1 n 1 + 1 n = ∏ n = 0 ∞ ( ∏ k = 0 n ( k + 1 ) ( - 1 ) k + 1 ( n k ) ) 1 n + 1 = {\Anzeigestil \stachel _{n=1}^{\einzigartig }{\frac {e^{\frac {1}{n}}}{1+{\frac {1}{n}}}}=\stachel _{n=0}^{\einzigartig }\links(\stachel _{k=0}^{{n}(k+1)^{(-1)^{{k+1}{n \wähle k}}\rechts)^{{\frac {1}{n+1}}=} $\prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}=$ ( 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 ... {\Anzeige-Stil \Text-Stil \links({\frac {2}{1}}}\rechts)^{1/2}\links({\frac {2^{{2}}{1\cPunkt 3}}}\rechts)^{1/3}\links({\frac {2^{3}\cPunkt 4}{1\cPunkt 3^{3}}}}}}}rechts)^{1/4}\links({\frac {2^{{4}\cPunkt 4^{{4}}}{1\cPunkt 3^{6}\cPunkt 5}}}}}rechts)^{{1/5}\Punkte } $\textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/5}\dots$	Prod[n=1 bis ∞]{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-Konstante	Eine {\a}Anzeigeart {A}} ${A}$	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 \grenzwerte _{n=0}^{\infty }{\frac {1}{n+1}}\sum \grenzwerte _{k=0}^{{n}\links(-1\rechts)^{k}{\binom {n}{k}}\links(k+1\rechts)^{2}\ln(k+1)}}} $e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	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	Schwarzschild Konische Konstante	e 2 {\Anzeigestil e^{2}}} $e^{2}$	∑ n = 0 ∞ 2 n n ! = 1 + 2 + 2 2 2 ! + 2 3 3 ! + 2 4 4 ! + 2 5 5 ! + ... {\darstellungsstil \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!}}+\punkte } $\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots$	Summe[n=0 bis ∞]{2^n/n!}	T	A072334	7;2,1,1,3,18,5,1,1,1,6,30,8,1,1,9,42,11,1,...] = [7,2,(1,1,n,4*n+6,n+2)], n = 3, 6, 9, usw.
1.01494160640965362502120255427452028	Gieseking-Konstante	G G i {\Anzeigestil {G_{Gi}}} ${G_{Gi}}$	3 3 4 ( 1 - ∑ n = 0 ∞ 1 ( 3 n + 2 ) 2 + ∑ n = 1 ∞ 1 ( 3 n + 1 ) 2 ) = {\displaystyle {\frac {{\sqrt {3}}}{4}}}\links(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}}\right)=} ${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ 3 3 4 ( 1 - 1 2 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± ... ) {\displaystyle \textstyle {\frac {\sqrt {3}}}{4}}}\links(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 \punkte \rechts)} $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)$ .		T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2.62205755429211981046483958989111941	Lemniscata-Konstante	ϖ {\displaystyle {\varpi }} ${\varpi }$	π G = 4 2 π ( 1 4 ! ) 2 {\displaystyle \pi \,{{G}=4{\sqrt {\tfrac {2}{\pi }}}\,({\tfrac {1}{4}}}!)^{2}}} $\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,({\tfrac {1}{4}}!)^{2}$	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-Konstante	G {\Anzeigestil {G}} ${G}$	1 a g m ( 1 , 2 ) = 4 2 ( 1 4 ! ) 2 π 3 / 2 A g m : A r i t d e r M e t t i k - g e o m e t r i k m e a n {\darstellungsstil {\Untermenge {\Agm:}Arithmetisch-geometrischer {\aagm}. (1,{\sqrt {2})}}{\frac {4\sqrt {2}!)}{3/2}}}}}} ${\underset {Agm:\;Arithmetic-geometric\;mean}{{\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}}}$	(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)} $\zeta (6)$	π 6 945 = ∏ n = 1 ∞ 1 1 - p n - 6 p n : p r i m o = 1 1 - 2 - 6 ⋅ 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}{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}}... } ${\frac {\pi ^{6}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}...$	Prod[n=1 bis ∞] {1/(1-ithprime(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 {\zeta {1}{\zeta (2)}}} ${\frac {1}{\zeta (2)}}$	6 π 2 = ∏ n = 0 ∞ ( 1 - 1 p n 2 ) p n : p r i m o = ( 1 - 1 2 2 ) ( 1 - 1 3 2 ) ( 1 - 1 5 2 ) ... {\darstellungsstil {\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\links(1-{\frac {1}{{p_{n}}^{2}}}}}}}}}{=}\Textart \links(1{-}{\frac {1}{2^{2}}}}}}rechts)\links(1{-}{\frac {1}{3^{2}}}}}}rechts)\links(1{-}{\frac {1}{5^{2}}}}}rechts)\Punkte } ${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)\dots$	Prod{n=1 bis ∞} (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	Das Verhältnis von Quadrat und umschriebenen oder eingeschriebenen Kreisen	π 2 2 {\displaystyle {\frac {\pi }{2{\sqrt {2}}}}} ${\frac {\pi }{2{\sqrt {2}}}}$	∑ n = 1 ∞ ( - 1 ) ⌊ n - 1 2 ⌋ 2 n + 1 = 1 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 - ... {\darstellungsstil \sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}}+{\frac {1}{11}}-\Punkte } $\sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots$	Summe[n=1 bis ∞]{(-1)^(Etage((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-Konstante	F {\Anzeigestil {F}} ${F}$	∫ 0 ∞ 1 Γ ( x ) d x . = e + ∫ 0 ∞ e - x π 2 + ln 2 x d 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} $\int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	N[int[0 bis ∞] {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	Quadratwurzel der Zahl e	e {\sqrt {\sqrt {e}} ${\sqrt {e}}$	∑ n = 0 ∞ 1 2 n n n ! = ∑ n = 0 ∞ 1 ( 2 n ) ! ! = 1 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}}}+{\frac {1}{2}}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots } $\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots$	Summe[n=0 bis ∞]{1/(2^n n!)}	T	A019774	[1;1,1,1,1,5,1,1,1,9,1,1,1,13,1,1,17,1,1,1,21,1,1,1,...] = [1;1,(1,1,4p+1)], p∈ℕ
i	Imaginäre Zahl	i {\a}Anzeige-Stil {i} ${i}$	- 1 = ln ( - 1 ) π e i π = - 1 {\displaystyle {\sqrt {-1}}={\frac {\ln(-1)}{\pi }\qquad \qquad \mathrm {e} ^i\,\pi {\pi}=-1} ${\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1$	sqrt(-1)	C
262537412640768743.999999999999250073	Hermite-Ramanujanische Konstante	R {\Anzeigestil {R}} ${R}$	e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} $e^{\pi {\sqrt {163}}}$	e^(π sqrt(163))	T	A060295	[262537412640768743;1,1333462407511,1,8,1,1,5,...]
4.81047738096535165547303566670383313	John-Konstante	γ {\displaystyle \gamma } $\gamma$	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}}} ${\sqrt[{i}]{i}}=i^{-i}=i^{\frac {1}{i}}=(i^{i})^{-1}=e^{\frac {\pi }{2}}$	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 {\darstellungsstil \alpha } $\alpha$	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 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 }} ${\frac {\pi }{ln(2)}}={\frac {\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}{-}{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-\dots }{{\frac {1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}-\dots }}$	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	Hyperbolische Tangente (1)	t h 1 {\darstellungsstil th\,1} $th\,1$	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}}}} ${\frac {e-{\frac {1}{e}}}{e+{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}$	(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	Fortgesetzte Fraktion konstant	C C F {\Anzeigestil {C}_{CF}} ${C}_{CF}$	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 = 0 ∞ 1 n ! n ! n ! = 0 1 1 + 1 1 1 + 2 4 + 3 36 + 4 576 + ... 1 1 1 + 1 1 1 + 1 4 + 1 36 + 1 576 + ... {\Darstellungsstil {\Untermenge {J_{k}(){Bessel}}{\underset {Funktion}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n}{n!n!Obergrenzen _{n=0}^{\infty }{\frac {\an8}{\an8}}1{n!n!}}}}={\frac {\frac {0}{1}}}+{\frac {1}{1}}}+{\frac {2}{4}}}+{\frac {3}{36}}}+{\frac {4}{576}}+\punkte }{\frac {1}{1}{1}}}+{\frac {1}{1}{1}{1}{1}{1}{1}}}+{\frac {1}{4}}}+{\frac {1}{576}}+\punkte }} ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(Summe {n=0 bis inf} n/(n!n!)) /(Summe {n=0 bis 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	Inverse Napier-Konstante	1 e {\displaystyle {\frac {1}{e}}} ${\frac {1}{e}}$	∑ n = 0 ∞ ( - 1 ) n n n ! = 1 0 ! - − 1 1 ! + 1 2 ! - − 1 3 ! + 1 4 ! - − 1 5 ! + ... {\darstellungsstil \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!}}}+\punkte } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots$	Summe[n=2 bis ∞]{(-1)^n/n!}	T	A068985	[0;2,1,1,1,2,1,1,1,4,1,1,1,6,1,1,8,1,1,1,10,1,1,1,12,...] = [0;2,1,(1,2p,1)], p∈ℕ
2.71828182845904523536028747135266250	Napier-Konstante	e {\Anzeigestil e} $e$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots$	Summe[n=0 bis ∞]{1/n!}	T	A001113	[2;1,2,1,1,1,4,1,1,1,6,1,1,1,8,1,1,1,10,1,1,1,12,1,...] = [2;(1,2p,1)], p∈ℕ
0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i	Faktorielles von i	i ! ...im Display-Stil. } $i\,!$	Γ ( 1 + i ) = i Γ ( i ) {\Anzeigestil \Gamma (1+i)=i\,\Gamma (i)} $\Gamma (1+i)=i\,\Gamma (i)$	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	Unendlich Durchdringung von i	∞ i {\ansichtsstil {}^{\infty }i} ${}^{\infty }i$	lim n → ∞ n i = lim n → ∞ i i i ⋅ ⋅ i ⏟ n {\Anzeigestil \lim _{n\bis \infty }{}^{n}i=\lim _{n\bis \infty }\unterbinde {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}} $\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	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 des Unendlichen Durchdringung von i	∞ i \| \| \| \| \| \| \| \| \| \| \| \| ∞ i \| \| \| \| \| \| \| \| \| \| \| \| \| $\|{}^{\infty }i\|$	lim n → ∞ \| n i \| = \| lim n → ∞ i i i ⋅ ⋅ i ⏟ n \| \| {\darstellungsstil \lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} {\an8}Richtig.} $\lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right\|$	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-Konstante	M {\ansichtsstil M} $M$	lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) Anzeigestil \lim _{n\rightarrow \infty \lefty \lefty {\frac {1}{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)} p $\lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)$ :..... Primzahlen			A077761	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]
1.9287800...	Wright-Konstante	ω {\omega \displaystyle \omega } $\omega$	⌊ 2 2 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle \links\floor 2^{2^{2^{{\cdot ^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor } $\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor$ = primos: {\displaystyle \quad } $\quad$ ⌊ 2 ω ⌋ {\Anzeigestil \links\Flur 2^{\omega }\rechts\Flur } $\left\lfloor 2^{\omega }\right\rfloor$ =3, ⌊ 2 2 ω ⌋ {\Anzeigestil \links\Flur 2^{2^{\omega }}\rechts\Flur } $\left\lfloor 2^{2^{\omega }}\right\rfloor$ =13, ⌊ 2 2 2 2 ω ⌋ {\Anzeigestil \links\floor 2^{2^{2^{{\omega }}}\rechts\floor } $\left\lfloor 2^{2^{2^{\omega }}}\right\rfloor$ =16381, ... {\Anzeigestil \dots } $\dots$			A086238	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
0.37395581361920228805472805434641641	Artin-Konstante	C A r t i n {\Anzeigestil C_{Artin}} $C_{Artin}$	∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\Anzeigestil \prod _{n=1}^{\infty }\links(1-{\frac {1}{p_{n}(p_{n}-1)}}}}rechts)} ......pn $\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)$ : prim		T	A005596	[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]
4.66920160910299067185320382046620161	Feigenbaum-Konstante δ	δ {\a6}Anzeige-Stil {\delta } ${\delta }$	lim n → ∞ x n + 1 - x n 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)} $\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ 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})} $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {o}\quad x_{n+1}=\,a\sin(x_{n})$		T	A006890	[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
2.50290787509589282228390287321821578	Feigenbaum-Konstante α	α {\darstellungsstil \alpha } $\alpha$	lim n → ∞ d n d n + 1 {\darstellungsstil \lim _{n\bis \infty }{\frac {d_{n}}{d_{n+1}}}} $\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$		T	A006891	[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
5.97798681217834912266905331933922774	Sechseckige Madelung Konstante ₂	H 2 ( 2 ) {\Anzeigestil H_{2}(2)} $H_{2}(2)$	π ln ( 3 ) 3 {\displaystyle \pi \ln(3){\sqrt {3}}} $\pi \ln(3){\sqrt {3}}$	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)} $\beta (3)$	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 + ... {\darstellungsstil {\frac {\pi ^{3}}{32}}}=\summe _{{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}}}{+}\Punkte } ${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\dots$	Summe[n=1 bis ∞]{(-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-Konstante ₂ = Σ Inverse Zwillings-Primzahlen	B 2 {\Anzeigestil B_{\,2}} $B_{\,2}$	∑ ( 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 ) + ... {\darstellungsstil \textstil \sum {\sum {\,\,p+2:\,{primos}}{{{\frac {1}{p}}}+{\frac {1}{p+2}}}}}}}=({\frac {1}{3}}{+}{\frac {1}{5}}})+({\frac {1}{5}}{+}{\frac {1}{7}}})+({\frac {1}{11}}{+}{\frac {1}{13}})+\punkte } $\textstyle \sum {\underset {p,\,p+2:\,{primos}}{({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+\dots$			A065421	[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
0.870588379975	Brun-Konstante ₄ = Σ Inverse der doppelten Primzahl	B 4 {\Anzeigestil B_{\,4}} $B_{\,4}$	( 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 ) + ... {\Anzeigestil {\Untermenge {p,\,p+2,\,p+4,\,p+6:{\,{Primes}}{\links({\frac {1}{5}}+{\frac {1}{7}}+{\frac {1}{11}}+{\frac {1}{13}}}\rechts)}}+\links({\frac {1}{11}}+{\frac {1}{13}}}+{\frac {1}{17}}+{\frac {1}{19}}\rechts)+\punkte } ${\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22.4591577183610454734271522045437350	Pi^e	π e {\displaystyle \pi ^{e}} $\pi ^{e}$	π e {\displaystyle \pi ^{e}} $\pi ^{e}$	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, Archimedische Konstante	π {\a6}Anzeige-Stil \pi } $\pi$	lim n → ∞ 2 n 2 - 2 + 2 + 2 ⋯ + 2 ⏟ n {\darstellungsstil \lim _{n\bis \infty }\,2^{n}\unterbinde {\sqrt {2-{\sqrt {2+{\sqrt {2+\punkte +{\sqrt {2}}}}}}}} _{n}} $\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}$	Summe[n=0 bis ∞]{(-1)^n 4/(2n+1)}	T	A000796	[3;7,15,1,292,1,1,1,2,1,3,1,14,...]
0.06598803584531253707679018759684642		e - e {\Anzeigestil e^{-e}} $e^{-e}$	e - e {\Anzeigestil e^{-e}} $e^{-e}$ ... Untere Grenze der Durchdringung		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 {\a}Anzeigeart i^{i}} $i^{i}$	e - π 2 {\displaystyle e^{\frac {-\pi }{2}}} $e^{\frac {-\pi }{2}}$	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	Bernstein-Konstante	β {\displaystyle \beta } $\beta$	1 2 π {\displaystyle {\frac {1}{2{\sqrt {\pi }}}}} ${\frac {1}{2{\sqrt {\pi }}}}$		T	A073001	[0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…]
0.28878809508660242127889972192923078	Flajolet und Richmond	Q {\Anzeigestil Q}	∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 2 2 2 ) ( 1 - 1 2 3 ) ... {\Anzeigestil \prod _{n=1}^{\infty }\links(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 } $\prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)\dots$	prod[n=1 bis ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Inverse von Pi, Ramanujan	1 π {\displaystyle {\frac {\pi {1}{\pi }}} ${\frac {1}{\pi }}$	2 2 9801 ∑ n = 0 ∞ ( 4 n ) ! ( 1103 + 26390 n ) ( n ! ) 4 396 4 n {\displaystyle {\frac {2{\sqrt {2}}}{9801}}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}} ${\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}$		T	A049541	[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...]
0.47494937998792065033250463632798297	Weierstraß-Konstante	W W W E {\Anzeigestil W_{_{WE}}} $W_{_{WE}}$	e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {\displaystyle {\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{42^{3/4}{({\frac {1}{4}}}!)^{2}}}}} ${\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{42^{3/4}{({\frac {1}{4}}!)^{2}}}}$	(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-Konstante	Ω {\Anzeigestil \Omega } $\Omega$	W ( 1 ) = ∑ n = 1 ∞ ( - n ) n - 1 n ! = 1 - 1 + 3 2 - 8 3 + 125 24 - ... {\darstellungsstil W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}}=1{-}1{+}{\frac {3}{2}}}{-}{\frac {8}{3}}}{+}{\frac {125}{24}}}-\punkte } $W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots$	Summe[n=1 bis ∞]{(-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	Eulersche Zahl	γ {\displaystyle \gamma } $\gamma$	- ψ ( 1 ) = ∑ n = 1 ∞ ∑ ∑ k = 0 ∞ ( - 1 ) k 2 n + k {\darstellungsstil -\psi (1)=\summe _{n=1}^{\infty }\summe _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{{n}+k}}}} $-\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}$	summe[n=1 bis ∞]\|summe[k=0 bis ∞]{((-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-Reihe	π 3 3 3 {\displaystyle {\frac {\pi }{3{\sqrt {3}}}}} ${\frac {\pi }{3{\sqrt {3}}}}$	∑ n = 1 ∞ 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n{2n \wähle n}}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots } $\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$	Summe[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 {\displaystyle {\frac {\pi {2}{\pi }}} ${\frac {2}{\pi }}$	2 2 ⋅ 2 + 2 2 2 ⋅ 2 + 2 + 2 + 2 2 2 ⋯ {\displaystyle {\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots } ${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
0.66016181584686957392781211001455577	Doppelte Primzahl-Konstante	C 2 {\Anzeigestil C_{2}} $C_{2}$	∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {\Anzeigestil \prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}} $\prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}$	prod[p=3 bis ∞]{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-Grenzkonstante	λ {\displaystyle \lambda } $\lambda$				A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0.69314718055994530941723212145817657	Logarithmus de 2	L n ( 2 ) {\Anzeigestil Ln(2)} $Ln(2)$	∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ⋯ {\darstellungsstil \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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots$	Summe[n=1 bis ∞]{(-1)^(n+1)/n}	T	A002162	[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...]
0.78343051071213440705926438652697546	Traum des Zweitklässlers ₁ J.Bernoulli	I 1 {\Anzeigestil I_{1}} $I_{1}$	∑ n = 1 ∞ ( - 1 ) n + 1 n n n = 1 - 1 2 2 + 1 3 3 - 1 4 4 + 1 5 5 + ... {\darstellungsstil \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}}}+\punkte } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots$	Summe[ -(-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 ) {\Anzeigestil \beta (1)} $\beta (1)$	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}{3}}}-{\frac {1}{3}}+{\frac {1}{5}}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots } ${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	Summe[n=0 bis ∞]{(-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	Handlungsreisender Nielsen-Ramanujan	ζ ( 2 ) 2 {\displaystyle {\frac {\zeta (2)}{2}}}} ${\frac {\zeta (2)}{2}}$	π 2 12 = ∑ n = 1 ∞ ( - 1 ) n + 1 n 2 = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\darstellungsstil {\frac {\pi ^{2}}{12}}}=\summe _{{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}}}-\Punkte } ${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots$	Summe[n=1 bis ∞]{((-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	Katalanische Konstante	C {\ansichtsstil C} $C$	∑ n = 0 ∞ ( - 1 ) n ( 2 n + 1 ) 2 = 1 1 2 - 1 3 2 + 1 5 2 - 1 7 2 + ⋯ {\darstellungsstil \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}}}+\ccdots } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots$	Summe[n=0 bis ∞]{(-1)^n/(2n+1)^2}	I	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1.05946309435929526456182529494634170	Verhältnis des Abstands zwischen Halbtönen	2 12 {\displaystyle {\sqrt[{12}]{2}}} ${\sqrt[{12}]{2}}$	2 12 {\displaystyle {\sqrt[{12}]{2}}} ${\sqrt[{12}]{2}}$	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}} $\zeta {4}$	π 4 90 = ∑ n = 1 ∞ 1 n 4 = 1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 + 1 5 4 + ... {\darstellungsstil {\frac {\pi ^{4}}{90}}}=\summe _{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}}}+\punkte } ${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+\dots$	Summe[n=1 bis ∞]{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 konstant	C V i {\i {\ansichtsstil C_{Vi}}} $C_{Vi}$	lim n → ∞ \| a n \| 1 n {\displaystyle \lim _{n\to \infty }\|a_{n}\|^{\frac {1}{n}}} $\lim _{n\to \infty }\|a_{n}\|^{\frac {1}{n}}$			A078416	[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]
1.20205690315959428539973816151144999	Apéry-Konstante	ζ ( 3 ) {\displaystyle \zeta (3)} $\zeta (3)$	∑ n = 1 ∞ 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 3 + 1 4 3 + 1 5 3 + ⋯ {\darstellungsstil \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}}}+\pünktchen \,\! } $\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots \,\!$	Summe[n=1 bis ∞]{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}}})} $\Gamma ({\tfrac {3}{4}})$	( − 1 + 3 4 ) ! {\Anzeigestil \links(-1+{\frac {3}{4}}}rechts)! } $\left(-1+{\frac {3}{4}}\right)!$	(-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	Favard-Konstante	3 4 ζ ( 2 ) {\displaystyle {\tfrac {3}{4}}\zeta (2)} ${\tfrac {3}{4}}\zeta (2)$	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)^{{{\frac {1}{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\punkte } ${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\dots$	Summe[n=1 bis ∞]{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	Kubikwurzel aus 2, Konstante Delian	2 3 {\ansichtsstil {\sqrt[{3}]{2}}} ${\sqrt[{3}]{2}}$	2 3 {\ansichtsstil {\sqrt[{3}]{2}}} ${\sqrt[{3}]{2}}$	2^(1/3)	I	A002580	[1;3,1,5,1,1,4,1,1,8,1,14,1,10,...]
1.29128599706266354040728259059560054	Traum des Zweitklässlers ₂ J.Bernoulli	I 2 {\Anzeigestil I_{2}} $I_{2}$	∑ n = 1 ∞ 1 n n n = 1 + 1 2 2 2 + 1 3 3 + 1 4 4 + 1 5 5 + 1 6 6 + ... {\darstellungsstil \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}}}}+\punkte } $\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}=1+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}+\dots$	Summe[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	Kunststoff-Nummer	ρ {\rho \rho \rho } $\rho$	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 }}}}}}}}} ${\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+\cdots }}}}}}}}$		I	A060006	[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...]
1.41421356237309504880168872420969808	Quadratwurzel aus 2, Pythagoras-Konstante	2 {\displaystyle {\sqrt {2}}} ${\sqrt {2}}$	∏ n = 1 ∞ 1 + ( - 1 ) n + 1 2 n - 1 = ( 1 + 1 1 1 ) ( 1 - 1 3 ) ( 1 + 1 5 ) . . . . {\Anzeigestil \prod _{n=1}^{\infty }1+{\frac {(-1)^{{n+1}}}{2n-1}}}=\links(1{+}{\frac {1}{1}{1}}}\rechts)\links(1{-}{\frac {1}{3}}}}}rechts)\links(1{+}{\frac {1}{5}}\rechts)... } $\prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\left(1{+}{\frac {1}{1}}\right)\left(1{-}{\frac {1}{3}}\right)\left(1{+}{\frac {1}{5}}\right)...$	prod[n=1 bis ∞]{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-Nummer	e 1 e {\darstellungsstil e^{\frac {1}{e}}}} $e^{\frac {1}{e}}$	e 1 / e {\Anzeigestil e^{1/e}} $e^{1/e}$ ... Obere Grenze der Durchdringung			A073229	[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
1.53960071783900203869106341467188655	Lieb'sche quadratische Eiskonstante	W 2 D {\Anzeigestil W_{2D}} $W_{2D}$	lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 {\darstellungsstil \lim _{n\to \infty }(f(n))^{{n^{-2}}=\links({\frac {4}{3}}}}rechts)^{\frac {3}{2}}}} $\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}$	(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	Walliser Produkt	π / 2 {\Anzeigestil \pi /2} $\pi /2$	∏ 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 {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {\frac {8}{9}}\cdots } $\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$		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 {\,B}}Anzeigeart E_{\,B}} $E_{\,B}$	∑ 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}}}}+{\frac {1}{3}}+{\frac {1}{7}}}+{\frac {1}{15}}}+\cdots \,\! } $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!$	Summe[n=1 bis ∞]{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, Goldener Schnitt	φ {\varphi \displaystyle \varphi } $\varphi$	1 + 5 2 = 1 + 1 + 1 + 1 + 1 + 1 + ⋯ {\displaystyle {\frac {1+{\sqrt {5}}}{2}}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}} ${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(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)} $\zeta (\,2)$	π 2 6 = ∑ n = 1 ∞ 1 n 2 = 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}}}+\ccdots } ${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	Summe[n=1 bis ∞]{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	Die quadratische Wiederholungskonstante von Somos	σ {\Anzeigestil \sigma } $\sigma$	1 2 3 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};2^{1/4};3^{1/8}\cdots } ${\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots$		T	A065481	[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
1.73205080756887729352744634150587237	Theodorus-Konstante	3 {\displaystyle {\sqrt {3}}} ${\sqrt {3}}$	3 {\displaystyle {\sqrt {3}}} ${\sqrt {3}}$	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 {\Anzeigestil R} $R$	1 + 2 + 3 + 4 + ⋯ {\displaystyle {\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}} ${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$			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-Konstante	Γ ( 1 2 ) {\displaystyle \Gamma ({\tfrac {1}{2}}})} $\Gamma ({\tfrac {1}{2}})$	π = ( − 1 2 ) ! {\displaystyle {\sqrt {\pi }}=\links(-{\frac {1}{2}}\rechts)! } ${\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!$	qrt (pi)	T	A002161	[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]
2.29558714939263807403429804918949038	Universelle parabolische Konstante	P 2 {\Anzeigestil P_{\,2}}} $P_{\,2}$	ln ( 1 + 2 ) + 2 {\Anzeigestil \ln(1+{\sqrt {2}}})+{\sqrt {2}}} $\ln(1+{\sqrt {2}})+{\sqrt {2}}$	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	Bronze-Nummer	σ R r r {\Anzeigestil \sigma _{\,Rr}} $\sigma _{\,Rr}$	3 + 13 2 = 1 + 3 + 3 + 3 + 3 + 3 + 3 + ⋯ {\displaystyle {\frac {3+{\sqrt {13}}}{2}}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}} ${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(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-Konstante2	2 ln γ {\displaystyle 2\,\ln \,\gamma } $2\,\ln \,\gamma$	π 2 6 ln ( 2 ) {\displaystyle {\frac {\pi ^{2}}{6\ln(2)}}} ${\frac {\pi ^{2}}{6\ln(2)}}$	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	Quadratwurzel aus 2 pi	2 π {\displaystyle {\sqrt {\pi {2\pi }}} ${\sqrt {2\pi }}$	2 π = lim n → ∞ n ! e n n n n n {\displaystyle {\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}} ${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}$	qrt (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-Konstante	G G G S {\Anzeigestil G_{_{{\,GS}}}} $G_{_{\,GS}}$	2 2 {\Anzeigestil 2^{\sqrt {2}}} $2^{\sqrt {2}}$	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	Chintchin-Konstante	K 0 {\Anzeigestil K_{\,0}}} $K_{\,0}$	∏ n = 1 ∞ [ 1 + 1 n ( n + 2 ) ] ln n / ln 2 {\displaystyle \prod _{n=1}^{\infty }\links[{1+{1 \over n(n+2)}}}rechts]^{\ln n/\ln 2}}} $\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	prod[n=1 bis ∞]{(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-Konstante	γ {\displaystyle \gamma } $\gamma$	e π 2 / ( 12 ln 2 ) {\displaystyle e^{\pi ^{2}/(12\ln 2)}} $e^{\pi ^{2}/(12\ln 2)}$	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	Reziproke Fibonacci-Konstante	Ψ {\Anzeigestil \Psi } $\Psi$	∑ n = 1 ∞ 1 F n = 1 1 + 1 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1 13 + ⋯ {\darstellungsstil \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 } $\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$			A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4.13273135412249293846939188429985264	Wurzel aus 2 e pi	2 e π {\displaystyle {\sqrt {2e\pi }}} ${\sqrt {2e\pi }}$	2 e π {\displaystyle {\sqrt {2e\pi }}} ${\sqrt {2e\pi }}$	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-Konstante	2 e {\Anzeigestil 2^{\,e}} $2^{\,e}$	2 e {\Anzeigestil 2^{e}} $2^{e}$	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 zum Quadrat	π 2 {\Anzeigestil \pi ^{2}} $\pi ^{2}$	6 ∑ n = 1 ∞ 1 n 2 = 6 1 2 + 6 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 } $6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots$	6 Summe[n=1 bis ∞]{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-Konstante	e π {\displaystyle e^{\pi }} $e^{\pi }$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	Summe[n=0 bis ∞]{(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]

Online-Bibliographie

Online-Enzyklopädie ganzzahliger Sequenzen (OEIS)
Simon Plouffe, Konstantentabellen
Die Seite von Xavier Gourdon und Pascal Sebah über Zahlen, mathematische Konstanten und Algorithmen
MatheKonstanten

Fragen und Antworten

F: Was ist eine mathematische Konstante?

A: Eine mathematische Konstante ist eine Zahl, die eine besondere Bedeutung für Berechnungen hat.

F: Was ist ein Beispiel für eine mathematische Konstante?

A: Ein Beispiel für eine mathematische Konstante ist ً, das das Verhältnis des Umfangs eines Kreises zu seinem Durchmesser darstellt.

F: Ist der Wert von ً immer derselbe?

A: Ja, der Wert von ً ist für jeden Kreis immer derselbe.

F: Sind mathematische Konstanten ganze Zahlen?

A: Nein, mathematische Konstanten sind normalerweise reelle, nicht-ganzzahlige Zahlen.

F: Woher kommen die mathematischen Konstanten?

A: Mathematische Konstanten stammen nicht wie physikalische Konstanten aus physikalischen Messungen.