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Matematisk konstant: Definition og eksempler (π, e, φ)

Lær hvad en matematisk konstant er – definition, betydning og eksempler på π, e og φ. Klare forklaringer og forståelige illustrationer.

Forfatter: Leandro Alegsa Oprettelsesdato: 17. september 2022 Seneste opdatering: 17. marts 2026

en.wikipedia.org · Public domain

En matematisk konstant er et tal, som har en særlig betydning for beregninger. F.eks. betyder konstanten π (udtales "pie") forholdet mellem en cirkels omkreds og dens diameter. Denne værdi er altid den samme for alle cirkler. En matematisk konstant er ofte et reelt, ikke-integralt tal af interesse.

I modsætning til fysiske konstanter stammer matematiske konstanter ikke fra fysiske målinger.

Hvad menes med en matematisk konstant?

Kort sagt er en matematisk konstant et tal med en fast, entydig værdi, som optræder igen og igen i matematiske formler, beviser og beregninger. En konstant kan være heltallig (fx 0 eller 1), men begrebet bruges oftest om specielle reelle eller komplekse tal, som har særlige egenskaber eller historisk betydning.

Vigtige eksempler

π (pi): Forholdet mellem en cirkels omkreds og diameter. Tilnærmede værdier: π ≈ 3,14159. π er et irrationelt og transcendents tal; der findes mange repræsentationer, fx uendelige rækker og produkter (Leibniz-rækken, Machin-formler, Gauss–Legendre-algoritmen m.fl.).
e (Eulers tal): Grundtallet for naturlige logaritmer. Definitioner: e = lim_{n→∞} (1 + 1/n)^n og e = sum_{k=0}^∞ 1/k!. Tilnærmelse: e ≈ 2,71828. e er også transcendental.
φ (det gyldne snit): φ = (1 + √5)/2 ≈ 1,61803. φ optræder i geometri, kunst og natur og er et algebraisk irrationelt tal (det er rod af x^2 − x − 1 = 0).
√2: Kvadratroden af 2, et klassisk eksempel på et irrationelt algebraisk tal: √2 ≈ 1,41421.
ζ(3) (Apéry's konstant): værdien af Riemann zeta-funktionen i 3, vist irrationel af Apéry.
Euler–Mascheroni konstanten γ: γ = lim_{n→∞} (sum_{k=1}^n 1/k − ln n). Det er ukendt om γ er rationel eller irrationel.

Egenskaber og klassifikation

Matematiske konstanter klassificeres ofte efter, om de er:

Rationelle (kan skrives som brøk a/b),
Irrationelle (kan ikke skrives som brøk),
Algebraiske (løsning af et polynomium med heltalskoefficienter), eller
Transcendente (ikke løsning af noget sådant polynomium).

Eksempelvis er √2 irrationel men algebraisk, mens e og π er begge transcendental (bevist respektivt af Hermite og Lindemann).

Hvordan optræder konstanter i matematikken?

Konstanter dukker op i mange grene af matematikken og anvendelser:

Geometri: π og φ
Analyse og differentialligninger: e, π og Euler–Mascheroni γ
Taldteori og kombinatorik: zeta-værdier, konstante summationer
Numerisk matematik og beregning: effektive algoritmer til højpræcisionsberegning af π og e

Hvordan bestemmes og beregnes konstanter?

Numerisk beregning bruger serier, produkter, integraler eller iterative algoritmer. For π findes effektive metoder som Gauss–Legendre og BBP-formlen (som også kan udtrække enkelte hexadecimale cifre uden at beregne alle forudgående cifre). For e bruges ofte rækken sum_{k=0}^∞ 1/k! til hurtig konvergens.

Forskellen fra fysiske konstanter

Som nævnt ovenfor kommer matematiske konstanter ikke fra målinger i naturen. En fysisk konstant (fx lysets hastighed i vakuum) måles og kan være genstand for eksperimentel usikkerhed; en matematisk konstant er derimod en teoretisk værdi bestemt af definitioner eller beviser.

Opsummering

En matematisk konstant er et fast tal med særlig betydning i matematikken. Nogle konstanter er velkendte og optræder i mange sammenhænge (π, e, φ), andre er mere specialiserede. De kan være rationelle, irrationelle, algebraiske eller transcendente, og deres beregning og studie er et centralt emne i både ren og anvendt matematik.

Vigtige matematiske konstanter

Følgende tabel indeholder nogle vigtige matematiske konstanter:

Navn	Symbol	Værdi	Betydning
Pi, Archimedes' konstant eller Ludof's tal	π	≈3.141592653589793	Et transcendentalt tal, der er forholdet mellem længden af en cirkels omkreds og dens diameter. Det er også arealet af enhedscirklen.
E, Napiers konstant eller Eulers tal (udtales "oilers")	e	≈2.718281828459045	Et transcendentalt tal, som er basen for naturlige logaritmer, og som undertiden kaldes "det naturlige tal".
Det gyldne snit	φ	5 + 1 2 ≈ 1.618 {\displaystyle {\frac {{\sqrt {5}}}+1}{2}}}\approx 1.618} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	Det er værdien af en større værdi divideret med en mindre værdi, hvis denne er lig med værdien af summen af værdierne divideret med den større værdi.
Kvadratroden af 2, Pythagoras' konstant	2 {\displaystyle {\sqrt {2}}}} ${\sqrt {2}}$	≈ 1.414 {\displaystyle \approx 1.414} $\approx 1.414$	Et irrationelt tal, der er længden af diagonalen i et kvadrat med sider af længden 1. Dette tal kan ikke skrives som en brøk.

Konstanter og serier

Følgende tabel indeholder en liste over konstanter og serier i matematikken med følgende kolonner:

Værdi: Numerisk værdi af konstanten.
LaTeX: Formel eller serie i TeX-format.
Formel: Til brug i programmer som Mathematica eller Wolfram Alpha.
OEIS: Link til On-Line Encyclopedia of Integer Sequences (OEIS), hvor konstanterne er tilgængelige med flere detaljer.
Fortsat fraktion: I den simple form [til heltal; frac1, frac2, frac3, ...] (i parentes hvis periodisk)
Type:

R - Rationalt tal
I - Irrationelt tal
T - Transcendentalt tal
C - komplekst tal

Bemærk, at listen kan ordnes tilsvarende ved at klikke på overskriften øverst i tabellen.

Værdi	Navn	Symbol	LaTeX	Formel	Type	OEIS	Fortsat brøkdel
3.24697960371746706105000976800847962	Sølv, Tutte-Beraha konstant	ς {\displaystyle \varsigma } $\varsigma$	2 + 2 cos ( 2 π / 7 ) = 2 + 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 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	Ramanujan indlejret radikal R₅	R 5 {\displaystyle R_{5}} $R_{5}$	5 + 5 + 5 + 5 - 5 + 5 + 5 + 5 + 5 + 5 - ⋯ = 2 + 5 + 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 {\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	Kvadratrod af 5, Gauss sum	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 til 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 {\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 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 til ∞]{(-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-konstant	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 til ∞]{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 + 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)^{(-1)^{k+1}{n \vælge 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 til ∞]{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 koniske 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 til ∞]{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, osv.
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 {\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 {\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 \pi \,{G}=4{\sqrt {\tfrac {\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 2 π 3 / 2 A g m : A r i t h m e t i k - g e o m e t r i k m e a n {\displaystyle {\underset {\underset {Agm:\;Aritmetisk-geometrisk\;mean}{{\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 1 - 5 - 6 . . . {\displaystyle {\frac {\pi ^{6}}}{945}}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}}{\frac {\frac {1}{{{1-p_{n}}}^{-6}}}}={\frac {1}{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 til ∞] {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 {\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 {\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 til ∞} (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	Forholdet mellem et kvadrat og omskrevne eller indskrevne cirkler	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 til ∞]{(-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-konstant	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 til ∞] {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	Kvadratrod af tallet e	e {{\displaystyle {\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}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 til ∞]{1/(2^n n!)}	T	A019774	[1;1;1,1,1,1,1,5,1,1,1,1,9,1,1,1,1,13,1,1,1,1,17,1,1,1,1,1,21,1,1,1,...] = [1;1,(1,1,1,4p+1)], p∈ℕ
i	Imaginært 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 = 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 {\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 e + 1 e = e 2 - 1 e 2 + 1 {\displaystyle {\frac {e-{\frac {1}{e}{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;1,3,5,7,7,9,11,13,15,17,19,21,23,25,27,...] = [0;(2p+1)], p∈ℕ
0.69777465796400798200679059255175260	Fortsat 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 = 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 {\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}}{\\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {{\frac {0}{1}{1}}}+{\frac {1}{1}{1}}}+{\frac {2}{4}{4}}}+{\frac {3}{36}}}+{\frac {4}{576}}}+\dots }{{\frac {1}{1}{1}}}+{\frac {1}{1}{1}}}+{\frac {1}{4}}}+{\frac {1}{36}}}+{\frac {1}{576}}+\dots }}} ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(sum {n=0 til inf} n/(n!n!)) /(sum {n=0 til inf} 1/(n!n!))		A052119	[0;1,2,3,4,5,5,6,7,7,8,8,9,10,11,12,13,14,15,16,...] = [0;(p+1)], p∈ℕ
0.36787944117144232159552377016146086	Omvendt Napier-konstant	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 til ∞]{(-1)^n/n!}	T	A068985	[0;2,1,1,1,2,1,1,1,4,1,1,1,1,6,1,1,1,8,1,1,1,1,10,1,1,1,1,12,...] = [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 til ∞]{1/n!}	T	A001113	[2;1;1,2,1,1,1,4,1,1,1,1,6,1,1,1,8,1,1,1,1,10,1,1,1,1,12,1,...] = [2;(1,2p,1)], p∈ℕ
0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i	Factorial af 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	Uendelig Tetration af i	∞ i {\displaystyle {}^{\infty }i} ${}^{\infty }i$	lim n → ∞ n i = lim n → ∞ i i ⋅ ⋅ ⋅ i ⏟ n {\displaystyle \lim _{n\til \infty }{}^{n}i=\lim _{n\til \infty }\underbrace {i^{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 af uendelig Tetration af i	\| ∞ i \| {\displaystyle \|{}^{{\infty }i\|} $\|{}^{\infty }i\|$	lim n → ∞ \| n i \| = \| lim n → ∞ i i ⋅ ⋅ ⋅ i ⏟ n \| {{\displaystyle \lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{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 ⋅ ⋅ 2 ω ⌋ {\displaystyle \left\lfloor 2^{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}(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	Feigenbaum-konstant δ	δ {\ {\displaystyle {\delta }} ${\delta }$	lim n → ∞ x n + 1 - x n x n + 2 - x n + 1 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-konstant 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 \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}{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 til ∞]{(-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 omvendt tvillingeprimtal	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	Brun-konstant₄ = Σ omvendt af tvillingeprimtal	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 {\undersæt {\underset {p,\,p+2,\,p+4,\,\,p+6:\,{primer}}{\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 + 2 + ⋯ + 2 ⏟ n {\displaystyle \lim _{n\til \infty }\,2^{n}\underbrace {\sqrt {2-{\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 til ∞]{(-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 grænse for 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	Bernstein-konstant	β {\displaystyle \beta } $\beta$	1 2 π {\displaystyle {\frac {\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 og 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 til ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Inverse af 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 {\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{-}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 til ∞]{(-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 til ∞]\|sum[k=0 til ∞]{((-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 { {\displaystyle {\frac {\frac {2}{\pi }}} ${\frac {2}{\pi }}$	2 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+{{{{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 til ∞]{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 Grænsekonstant	λ {\displaystyle \lambda } $\lambda$				A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0.69314718055994530941723212145817657	Logaritme 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 til ∞]{(-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 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 - 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 til ∞]{(-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	Rejsende handelsrepræsentant 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}{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 til ∞]{((-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	Catalansk konstant	C {\displaystyle C} $C$	∑ n = 0 ∞ ( - 1 ) n ( 2 n + 1 ) 2 = 1 1 2 1 2 - 1 3 2 + 1 5 2 - 1 7 2 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {(-1)^{n}}}{(2n+1)^{2}}}}}={\frac {\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 til ∞]{(-1)^n/(2n+1)^2}	I	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1.05946309435929526456182529494634170	Forholdet mellem afstanden mellem halvtoner	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}{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 til ∞]{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 Archived 2013-04-13 at te Wayback Machine constant	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	Apéry konstant	ζ ( 3 ) {\displaystyle \zeta (3)} $\zeta (3)$	∑ n = 1 ∞ 1 n 3 = 1 1 1 3 + 1 2 3 + 1 3 3 3 + 1 4 3 + 1 5 3 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{3}}}}}={\frac {1}{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 til ∞]{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	Favard-konstant	3 4 ζ ( 2 ) {\displaystyle {\tfrac {\tfrac {3}{4}}}\zeta (2)} ${\tfrac {3}{4}}\zeta (2)$	π 2 8 = ∑ n = 0 ∞ 1 ( 2 n - 1 ) 2 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 til ∞]{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	Kubusrod af 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 1 2 2 + 1 3 3 + 1 4 4 4 + 1 5 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+{\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	Kvadratrod af 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}{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 til ∞]{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}}} $e^{1/e}$ ... Øvre grænse for 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-produkt	π / 2 {\displaystyle \pi /2} $\pi /2$	∏ n = 1 ∞ ( 4 n 2 4 n 2 4 n 2 - 1 ) = 2 1 ⋅ 2 3 ⋅ 4 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}{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 til ∞]{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, det gyldne snit	φ {\displaystyle \varphi } $\varphi$	1 + 5 2 = 1 + 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}{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 til ∞]{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' kvadratiske gentagelseskonstant	σ {\displaystyle \sigma } $\sigma$	1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {\sqrt {\sqrt {1{\sqrt {2{\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 {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	Universel 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	Bronze nummer	σ R r {\displaystyle \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-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	kvadratrod af 2 pi	2 π { {\displaystyle {\sqrt {2\pi }}} ${\sqrt {2\pi }}$	2 π = lim n → ∞ n ! e n 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-konstant	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 til ∞]{(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 + 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	Rod af 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 til ∞]{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 til ∞]{(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]

Relaterede sider

Konstant funktion
Liste over matematiske symboler

Bøger

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

Daniel Zwillinger (2012). Matematiske standardtabeller og 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 encyklopædi af hele talrækker (OEIS)
Simon Plouffe, tabeller over konstanter
Xavier Gourdon og Pascal Sebah's side med tal, matematiske konstanter og algoritmer
MathConstants

Spørgsmål og svar

Spørgsmål: Hvad er en matematisk konstant?

A: En matematisk konstant er et tal, der har en særlig betydning for beregninger.

Q: Hvad er et eksempel på en matematisk konstant?

A: Et eksempel på en matematisk konstant er ً, som repræsenterer forholdet mellem en cirkels omkreds og dens diameter.

Spørgsmål: Er værdien af ً altid den samme?

Svar: Ja, værdien af ً er altid den samme for enhver cirkel.

Spørgsmål: Er matematiske konstanter integrale tal?

Svar: Nej, matematiske konstanter er normalt reelle, ikke-integrale tal.

Spørgsmål: Hvor kommer matematiske konstanter fra?

Svar: Matematiske konstanter stammer ikke fra fysiske målinger, som fysiske konstanter gør.

Forfatter

AlegsaOnline.com - Matematisk konstant - Leandro Alegsa

Oprettelsesdato: 17. september 2022
Seneste opdatering: 17. marts 2026

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