Matematisk konstant: definition, typer och betydelse

Översikt av vad en matematisk konstant är, vanliga exempel, typer (irrationell, transcendent), historik, användningsområden och skillnader mot fysiska konstanter.

Författare: Leandro Alegsa Skapad: 17 september 2022 Uppdaterad: 27 april 2026

Matematisk konstant är ett tal som uppträder återkommande i matematiska samband och behåller samma värde oberoende av mätningar eller fysiska omständigheter. Begreppet omfattar enkla värden liksom tal som definieras genom serier, gränsvärden eller lösningar av ekvationer. En orienterande introduktion till termen finns under matematisk konstant.

Bildgalleri

3 Bilder

en.wikipedia.org · Public domain

Egenskaper och kategorier

Matematiska konstanter kan klassificeras efter algebraiska och analytiska egenskaper. Vanliga klasser är:

Irrationella tal: tal som inte kan uttryckas som ett bråk med heltal.
Transcendenta tal: tal som inte är rot till någon icke-nollig polynomekvation med heltalskoefficienter.
Algebraiska tal: motsatsen till transcendent—lösningar till polynom med heltalskoefficienter.
Konstanter definierade genom gränsvärden, integraler, oändliga serier eller produkter.

Exempel och praktiska roller

Flera välkända konstanter förekommer ofta i matematik och naturvetenskap. Till exempel betecknar π förhållandet mellan en cirkels omkrets och dess diameter. Konstanten e fungerar som bas för naturliga logaritmer och är central i analys och differentialekvationer. Andra exempel är det gyllene snittet, speciella zeta- eller gammavärden och konstanter som uppträder i kaotiska system. Vissa konstanter används som mått på komplexitet, som randvillkoren i problemlösning, eller som invarianta värden i geometri och talteori.

Historik och utveckling

Intresset för specifika konstanta värden sträcker sig långt tillbaka: antika civilisationer uppskattade π i samband med geometriska beräkningar. Under 1600–1800-talen växte förståelsen när analys och serienära representationer utvecklades. Med datorer har beräkningen av stora mängder decimaler blivit ett område både för test av algoritmer och för att studera egenskaper som slumpmässighet i decimalutvecklingen.

Användningar och betydelse

Matematiska konstanter har både teoretiska och praktiska tillämpningar. Teoretiskt ger de fasta referenspunkter i bevis och definitioner; praktiskt används de inom ingenjörsvetenskap, kryptografi, sannolikhetsteori och fysikaliska modeller där matematiska idealiseringar införs. Ibland definieras konstanter explicit för att koda information eller skapa konstruktioner med särskilda egenskaper.

Skillnad mot fysiska konstanter och intressanta fakta

Till skillnad från fysiska konstanter grundas matematiska konstanter på definitioner och logiska relationer snarare än experimentella mätningar. Många frågor om konstanters natur är fortfarande öppna: om deras decimaler är "normala" (dvs. statistiskt slumpmässiga) är okänt för de flesta, och flera konstanter har egenskaper som bara delvis förstås. Studiet av konstanter berör områden som talteori, analys, dynamiska system och datalogi.

Sammanfattningsvis utgör matematiska konstanter fasta, definierbara tal som spelar nyckelroller i både abstrakta teorier och konkreta tillämpningar. De länkar historiska matematiska frågor med moderna beräkningsmetoder och fortsatt forskning.

Viktiga matematiska konstanter

Följande tabell innehåller några viktiga matematiska konstanter:

Namn	Symbol	Värde	Betydelse
Pi, Archimedes konstant eller Ludophs tal	π	≈3.141592653589793	Ett transcendentalt tal som är förhållandet mellan längden på en cirkels omkrets och dess diameter. Det är också enhetscirkelns area.
E, Napiers konstant eller Eulers tal (uttalas "oilers").	e	≈2.718281828459045	Ett transcendentalt tal som är basen för naturliga logaritmer, ibland kallat "naturligt tal".
Det gyllene snittet	φ	5 + 1 2 ≈ 1.618 {\displaystyle {\frac {{\sqrt {5}}+1}{2}}\approx 1.618} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	Det är värdet av ett större värde dividerat med ett mindre värde om detta är lika med värdet av summan av värdena dividerat med det större värdet.
Kvadratroten av 2, Pythagoras konstant	2 {\displaystyle {\sqrt {2}}}} ${\sqrt {2}}$	≈ 1.414 {\displaystyle \approx 1.414} $\approx 1.414$	Ett irrationellt tal som är längden på diagonalen i en kvadrat med sidor av längden 1. Detta tal kan inte skrivas som en bråkdel.

Konstanter och serier

Följande tabell innehåller en förteckning över konstanter och serier inom matematiken med följande kolumner:

Värde: Numeriskt värde för konstanten.
LaTeX: Formel eller serie i TeX-format.
Formel: För användning i program som Mathematica eller Wolfram Alpha.
OEIS: Länk till On-Line Encyclopedia of Integer Sequences (OEIS), där konstanterna finns tillgängliga med mer information.
Fortsatt fraktion: I enkel form [till heltal; frac1, frac2, frac3, ...] (inom parentes om periodisk)
Typ:

R - Rationellt tal
I - Irrationellt tal
T - transcendentalt tal
C - Komplext tal

Observera att listan kan ordnas på motsvarande sätt genom att klicka på rubriken högst upp i tabellen.

Värde	Namn	Symbol	LaTeX	Formel	Typ	OEIS	Fortsatt fraktion
3.24697960371746706105000976800847962	Silver, Tutte-Beraha konstant	ς {\displaystyle \varsigma } $\varsigma$	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 }}}}}}}}} $2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}$	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	Paris konstant	C P a {\displaystyle C_{Pa}} $C_{Pa}$	∏ n = 2 ∞ 2 φ φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}} $\prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}$		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}} $R_{5}$	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}}} $\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(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	Kvadratrot av 5, Gauss-summa	5 {\displaystyle {\sqrt {5}}} ${\sqrt {5}}$	∀ 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}}}} $\scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	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}}})} $\Gamma ({\tfrac {1}{4}})$	4 ( 1 4 ) ! = ( - 3 4 ) ! {\displaystyle 4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!} $4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	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}}} $C_{_{MRB}}$	∑ 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 } $\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots$	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 }} ${\rho }$	∏ 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 } $\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)\dots$	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 }} $e^{\gamma }$	∏ 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}}}=} $\prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}=$ ( 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 ⋅ $\textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/5}\dots$	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}} ${A}$	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)}} $e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	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}} $e^{2}$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots$	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}}} ${G_{Gi}}$	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)=} ${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ 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)} $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)$ .		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 }} ${\varpi }$	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-konstant	G {\displaystyle {G}} ${G}$	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}}}}}} ${\underset {Agm:\;Arithmetic-geometric\;mean}{{\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}}}$	(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 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}}}}...} ${\frac {\pi ^{6}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}...$	Prod[n=1 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)}}} ${\frac {1}{\zeta (2)}}$	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 } ${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)\dots$	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}}}}} ${\frac {\pi }{2{\sqrt {2}}}}$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots$	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}} ${F}$	∫ 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} $\int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	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}}} ${\sqrt {e}}$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots$	sum[n=0 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}} ${i}$	- 1 = ln ( - 1 ) π e i π = - 1 {\displaystyle {\sqrt {-1}}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1} ${\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1$	sqrt(-1)	C
262537412640768743.999999999999250073	Hermite-Ramanujan-konstant	R {\displaystyle {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 konstant	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 {\\displaystyle \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 - 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	Hyperbolisk tangent (1)	t h 1 {\displaystyle 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	Fortsatt Fraktionskonstant	C C F {\displaystyle {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 ! 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 }} ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(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}}}} ${\frac {1}{e}}$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots$	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} $e$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots$	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\,!} $i\,!$	Γ ( 1 + i ) = i Γ ( i ) {\displaystyle \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	Oändlig Tetration av i	∞ i {\displaystyle {}^{\infty }i} ${}^{\infty }i$	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}} $\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	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\|} $\|{}^{\infty }i\|$	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\|} $\lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right\|$	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} $M$	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)} $\lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)$ ..... 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 } $\omega$	⌊ 2 2 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{2^{2^{\cdot ^{\cdot ^{2^{{\omega }}}}}}\right\rfloor } $\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor$ = primos: {\\displaystyle \quad } $\quad$ ⌊ 2 ω ⌋ {\displaystyle \left\lfloor 2^{\omega }\right\rfloor } $\left\lfloor 2^{\omega }\right\rfloor$ =3, ⌊ 2 2 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{{omega }}\right\rfloor } $\left\lfloor 2^{2^{\omega }}\right\rfloor$ =13, ⌊ 2 2 2 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{2^{2^{\omega }}}\right\rfloor } $\left\lfloor 2^{2^{2^{\omega }}}\right\rfloor$ =16381, ... {\displaystyle \dots } $\dots$			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}} $C_{Artin}$	∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)} $\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)$ ...... p_n : 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 }} ${\delta }$	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)} $\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ 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	Feigenbaumkonstanten α	α {\\displaystyle \alpha } $\alpha$	lim n → ∞ d n d n d n + 1 {\displaystyle \lim _{n\to \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	Hexagonal Madelung Constant ₂	H 2 ( 2 ) {\displaystyle 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 + ... {\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 } ${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\dots$	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}} $B_{\,2}$	∑ ( 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 } $\textstyle \sum {\underset {p,\,p+2:\,{primos}}{({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+\dots$			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}} $B_{\,4}$	( 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 } ${\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			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, Archimedes konstant	π {\\displaystyle \pi } $\pi$	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}} $\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}$	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}} $e^{-e}$	e - e {\displaystyle e^{-e}} $e^{-e}$ ... 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}} $i^{i}$	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	Bernsteins konstant	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 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 } $\prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)\dots$	prod[n=1 till ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Invers av Pi, Ramanujan	1 π {\displaystyle {\frac {\frac {1}{\pi }}} ${\frac {1}{\pi }}$	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}}}} ${\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}$		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}}} $W_{_{WE}}$	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-konstant	Ω {\displaystyle \Omega } $\Omega$	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 } $W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots$	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 } $\gamma$	- 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}}}} $-\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}$	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}}}}} ${\frac {\pi }{3{\sqrt {3}}}}$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$	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 }}} ${\frac {2}{\pi }}$	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 } ${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
0.66016181584686957392781211001455577	Twin prime konstant	C 2 {\displaystyle C_{2}} $C_{2}$	∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {\displaystyle \prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}} $\prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}$	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 } $\lambda$				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)} $Ln(2)$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots$	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}} $I_{1}$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots$	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)} $\beta (1)$	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 } ${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	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}}} ${\frac {\zeta (2)}{2}}$	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 } ${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots$	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} $C$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots$	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}}}} ${\sqrt[{12}]{2}}$	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 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 } ${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+\dots$	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}} $C_{Vi}$	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	Konstant apérium	ζ ( 3 ) {\displaystyle \zeta (3)} $\zeta (3)$	∑ 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 \,\!} $\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots \,\!$	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}})} $\Gamma ({\tfrac {3}{4}})$	( - 1 + 3 4 ) ! {\displaystyle \left(-1+{\frac {3}{4}}\right)!} $\left(-1+{\frac {3}{4}}\right)!$	(-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)} ${\tfrac {3}{4}}\zeta (2)$	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 } ${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\dots$	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}}}} ${\sqrt[{3}]{2}}$	2 3 {\displaystyle {\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	Sophomore's Dream₂ J.Bernoulli	I 2 {\displaystyle I_{2}} $I_{2}$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}=1+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}+\dots$	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 } $\rho$	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	Kvadratroten av 2, Pythagoras konstant	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 ) . . . {\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)...} $\prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\left(1{+}{\frac {1}{1}}\right)\left(1{-}{\frac {1}{3}}\right)\left(1{+}{\frac {1}{5}}\right)...$	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}}}} $e^{\frac {1}{e}}$	e 1 / e {\displaystyle e^{1/e}} $e^{1/e}$ ... 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}} $W_{2D}$	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}}}} $\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}$	(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} $\pi /2$	∏ 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 } $\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$		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}} $E_{\,B}$	∑ 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 \,\!} $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!$	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 } $\varphi$	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 }}}}}}}}} ${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(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 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 } ${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	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 } $\sigma$	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 } ${\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots$		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}}} ${\sqrt {3}}$	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 {\displaystyle 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 konstant	Γ ( 1 2 ) {\displaystyle \Gamma ({\tfrac {1}{2}})} $\Gamma ({\tfrac {1}{2}})$	π = ( - 1 2 ) ! {\displaystyle {\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!} ${\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!$	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}} $P_{\,2}$	ln ( 1 + 2 ) + 2 {\displaystyle \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	Brons nummer	σ R r {\displaystyle \sigma _{\,Rr}} $\sigma _{\,Rr}$	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 }}}}}}}}} ${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(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-konstant₂	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	kvadratroten av 2 pi	2 π {\displaystyle {\sqrt {2\pi }}} ${\sqrt {2\pi }}$	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}}}}} ${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}$	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}}} $G_{_{\,GS}}$	2 2 2 {\displaystyle 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	Khintchin konstant	K 0 {\displaystyle K_{\,0}} $K_{\,0}$	∏ 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}}} $\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	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 } $\gamma$	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	Reciprok Fibonacci-konstant	Ψ {\displaystyle \Psi } $\Psi$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$			A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4.13273135412249293846939188429985264	Rot av 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 konstant	2 e {\displaystyle 2^{\,e}} $2^{\,e}$	2 e {\displaystyle 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 i kvadrat	π 2 {\displaystyle \pi ^{2}} $\pi ^{2}$	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 } $6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots$	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 }} $e^{\pi }$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	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,...]

Relaterade sidor

Konstant funktion
Förteckning över matematiska symboler

Böcker

Finch, Steven (2003). Matematiska konstanter. Cambridge University Press. ISBN 0-521-81805-2.

Daniel Zwillinger (2012). Matematiska standardtabeller och formler. Imperial College Press. ISBN 978-1-4398-3548-7.

Eric W. Weisstein (2003). CRC Concise Encyclopedia of Mathematics. Chapman & Hall/CRC. ISBN 1-58488-347-2.

Lloyd Kilford (2008). Modular Forms, a Classical and Computational Introduction. Imperial College Press. ISBN 978-1-84816-213-6.

Online-bibliografi

On-Line Encyclopedia of Integer Sequences (OEIS)
Simon Plouffe, tabeller med konstanter
Xavier Gourdon och Pascal Sebahs sida med siffror, matematiska konstanter och algoritmer.
MathConstants

Frågor och svar

F: Vad är en matematisk konstant?

S: En matematisk konstant är ett tal som har en särskild betydelse för beräkningar.

F: Vad är ett exempel på en matematisk konstant?

S: Ett exempel på en matematisk konstant är ً, som representerar förhållandet mellan en cirkels omkrets och dess diameter.

F: Är värdet på ً alltid detsamma?

Svar: Ja, värdet av ً är alltid detsamma för alla cirklar.

Fråga: Är matematiska konstanter integrala tal?

Svar: Nej, matematiska konstanter är vanligtvis verkliga, icke-integrala tal.

F: Varifrån kommer matematiska konstanter?

S: Matematiska konstanter kommer inte från fysiska mätningar som fysiska konstanter gör.

Författare

AlegsaOnline.com Matematisk konstant: definition, typer och betydelse Leandro Alegsa

URL: https://sv.alegsaonline.com/art/126382

Så citerar du den här artikeln

APA

Alegsa, L. (27 april 2026). Matematisk konstant: definition, typer och betydelse. AlegsaOnline.com. https://sv.alegsaonline.com/art/126382

MLA

Alegsa, Leandro. “Matematisk konstant: definition, typer och betydelse.” AlegsaOnline.com, 27 april 2026, https://sv.alegsaonline.com/art/126382

Chicago

Alegsa, Leandro. “Matematisk konstant: definition, typer och betydelse.” AlegsaOnline.com. Uppdaterad 27 april 2026. https://sv.alegsaonline.com/art/126382

BibTeX

@misc{alegsaonline_126382,
  author = {Alegsa, Leandro},
  title = {Matematisk konstant: definition, typer och betydelse},
  year = {2026},
  howpublished = {AlegsaOnline.com},
  url = {https://sv.alegsaonline.com/art/126382},
  note = {Uppdaterad: 27 april 2026; Language: sv}
}

TXT

Leandro Alegsa. “Matematisk konstant: definition, typer och betydelse.” AlegsaOnline.com. Uppdaterad: 27 april 2026. https://sv.alegsaonline.com/art/126382