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Wiskundige constanten: definitie, voorbeelden (π, e, φ) en belang

Ontdek wat wiskundige constanten zijn, waarom π, e en φ belangrijk zijn, met heldere voorbeelden en toepassingen voor wiskunde en wetenschap.

Schrijver: Leandro Alegsa Aanmaakdatum: 20 mei 2021 Laatste update: 2 februari 2026

en.wikipedia.org · Public domain

Een wiskundige constante is een getal dat een speciale betekenis heeft voor berekeningen. Zo betekent de constante π (uitgesproken als "taart") de verhouding tussen de omtrek van een cirkel en zijn diameter. Deze waarde is altijd hetzelfde voor elke cirkel. Een wiskundige constante is vaak een reëel, niet-integraal getal van belang.

In tegenstelling tot fysische constanten komen wiskundige constanten niet voort uit fysische metingen.

Wat verstaan we onder wiskundige constanten?

Een wiskundige constante is een specifiek reëel of complex getal dat op meerdere plaatsen in de wiskunde terugkeert en waarvoor een vaste, universele waarde geldt. Zulke constanten ontstaan uit definities, limieten, reeksen, geometrische verhoudingen of oplossingen van algebraïsche vergelijkingen. Ze zijn onafhankelijk van fysieke eenheden of experimentele fouten: hun waarde is een zuiver wiskundig gegeven.

Belangrijke eigenschappen en classificatie

Rationeel vs. irrationeel: een rationaal getal kan als breuk p/q worden geschreven; veel wiskundige constanten (zoals π, e en φ) zijn irrationeel: ze hebben een oneindige, niet-periodieke decimale expansie.
Algebraïsch vs. transcendent: een algebraïsch getal is wortel van een niet‑nul veelterm met gehele coëfficiënten. Een transcendent getal is dat niet. Voorbeelden: φ is algebraïsch (wortel van x² − x − 1), terwijl π en e transcendent zijn.
Representaties: constanten kunnen worden uitgedrukt als oneindige reeksen, integraaluitdrukkingen, continue breuken of limieten. Sommige representaties zijn nuttig voor theoretische redenen, andere voor numerieke berekening.

Voorbeelden: π, e en φ

π (pi): verhouding omtrek : diameter van een cirkel. Numerieke waarde: π ≈ 3,141592653589793... Belangrijke eigenschappen: π is irrationeel en transcendentaal (Lindemann, 1882). π verschijnt overal in meetkunde, analyse, Fouriertransformaties, waarschijnlijkheid en natuurkunde. Bekende formule: Euler's identiteit e^{iπ} + 1 = 0.
e (Euler's getal): basis van de natuurlijke logaritme en limiet van (1 + 1/n)^n voor n → ∞. Numerieke waarde: e ≈ 2,718281828459045... e is transcendentaal (Hermite, 1873). e komt voor bij groei- en vervalprocessen, calculus (bijvoorbeeld bij integralen en afgeleiden van de exponentiële functie) en in kansrekening.
φ (gulden snede): φ = (1 + √5) / 2 ≈ 1,618033988749895... φ is irrationeel en algebraïsch (oplossing van x² − x − 1 = 0). De gulden snede verschijnt in de meetkunde van regelmatige veelhoeken (bijv. pentagon), in de limiet van verhoudingen van opeenvolgende Fibonacci-getallen en in optimale verhoudingen in architectuur en kunst.

Manieren om constanten te berekenen of te representeren

Oneindige reeksen: e = Σ_{n=0}^∞ 1/n!; voor π bestaan reeksen zoals de Leibniz‑serie π/4 = 1 − 1/3 + 1/5 − 1/7 + ... (weliswaar langzaam convergerend) en vele snellere Machin‑achtige formules op basis van arctan.
Limieten en producten: sommige constanten verschijnen als limieten (bijv. de definitie van e) of als oneindige producten (bijv. de Wallis-product voor π).
Continue breuken: de gulden snede heeft de eenvoudige continue breuk [1;1,1,1,...], wat de steeds herhalende structuur verklaart.
Numerieke algoritmen: voor hoge precisie worden speciale algoritmen gebruikt, zoals het Gauss–Legendre-algoritme voor π of moderne snel convergerende reeksen en transformaties.

Toepassingen en waarom ze belangrijk zijn

Wiskundige constanten spelen een sleutelrol in theorie en praktijk:

Theoretische wiskunde: constanten verbinden verschillende deelgebieden (analyse, getaltheorie, combinatoriek) en verschijnen in centrale stellingen en identiteiten.
Toegepaste wetenschap: π en e komen veel voor in natuurkunde, techniek, statistiek, signaalverwerking en probabiliteitsmodellen. De kennis van hun eigenschappen maakt nauwkeurige modellen en berekeningen mogelijk.
Computatie en cryptografie: sommige constanten en hun eigenschappen (zoals periodieke of niet‑periodieke patronen) zijn relevant voor algoritmische berekening en voor het testen van rekenmachines en willekeurigheidstests.
Culturele en historische waarde: constanten zoals π en de gulden snede hebben ook invloed gehad op wetenschapsgeschiedenis, kunst, architectuur en populaire wetenschap.

Andere bekende wiskundige constanten

γ (Euler–Mascheroni‑constante) ≈ 0,57721… (verschil tussen harmonische reeks en ln n)
ζ(3) (Apéry's constante) ≈ 1,2020569…, bekend uit getaltheorie; Apéry bewees de irrationaliteit van ζ(3)
Catalan's constante G ≈ 0,915965… die voorkomt in combinatorische sommen en speciale integralen

Slotopmerkingen

Wiskundige constanten zijn meer dan een verzameling getallen: ze zijn bouwstenen van wiskundige structuren en hulpmiddelen voor zowel theoretische inzichten als praktische toepassingen. Het bestuderen van hun eigenschappen (zoals rationaliteit, algebraïsche relaties en wijze van optreden in formules) levert vaak diepere inzichten op in de onderliggende wiskunde.

Belangrijkste wiskundige constanten

De volgende tabel bevat enkele belangrijke wiskundige constanten:

Naam	Symbool	Waarde	Betekenis
Pi, de constante van Archimedes of het getal van Ludoph	π	≈3.141592653589793	Een transcendentaal getal dat de verhouding is tussen de lengte van de omtrek van een cirkel en zijn diameter. Het is ook de oppervlakte van de eenheidscirkel.
E, de constante van Napier of het getal van Euler.	e	≈2.718281828459045	Een transcendentaal getal dat de basis is van natuurlijke logaritmen, ook wel het "natuurlijke getal" genoemd.
Gulden snede	φ	5 + 1 2 ≈ 1,618 {frac {{\sqrt {5}}+1}{2}}}approx 1,618} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	Het is de waarde van een grotere waarde gedeeld door een kleinere waarde als deze gelijk is aan de waarde van de som van de waarden gedeeld door de grotere waarde.
Vierkantswortel van 2, de constante van Pythagoras	2 {displaystyle {2}}} ${\sqrt {2}}$	≈ 1.414} $\approx 1.414$	Een irrationeel getal dat de lengte is van de diagonaal van een vierkant met zijden van lengte 1. Dit getal kan niet als breuk worden geschreven.

Constanten en reeksen

De volgende tabel bevat een lijst van constanten en reeksen in de wiskunde, met de volgende kolommen:

Waarde: Numerieke waarde van de constante.
LaTeX: Formule of reeks in TeX formaat.
Formule: Voor gebruik in programma's zoals Mathematica of Wolfram Alpha.
OEIS: Link naar On-Line Encyclopedia of Integer Sequences (OEIS), waar de constanten beschikbaar zijn met meer details.
Vervolgfractie: In de eenvoudige vorm [naar geheel getal; frac1, frac2, frac3, ...] (tussen haakjes indien periodiek)
Type:

R - Rationaal getal
I - Irrationeel getal
T - transcendentaal getal
C - Complex getal

Merk op dat de lijst dienovereenkomstig kan worden geordend door te klikken op de koptitel bovenaan de tabel.

Waarde	Naam	Symbool	LaTeX	Formule	Type	OEIS	Voortgezette fractie
3.24697960371746706105000976800847962	Zilver, Tutte-Beraha constant	ς {displaystyle \varsigma } $\varsigma$	2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 7 + 7 + 7 7 + ⋯ 3 3 3 1 + 7 + 7 7 + 7 7 + ⋯ 3 3 3 {\displaystyle 2+2cos(2 π /7)=textstyle 2+{{\sqrt[{3}]{7+7{{sqrt[{3}]{7+7{{sqrt[{3}]{7,7+\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	Parijs constant	C P a {{Pa}} $C_{Pa}$	∏ n = 2 ∞ 2 φ φ + φ n , φ = F i {{n=2}^{infty }{frac {2varphi }{{varphi +varphi _{n}}};, φvarphi ={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 geneste radicaal R₅	R 5 {\displaystyle R_{5}} $R_{5}$	5 + 5 + 5 - 5 + 5 + 5 - ⋯ = 2 + 5 + 15 - 6 5 2 {\displaystyle {\scriptstyle {5+{sqrt {5+{sqrt {5-{sqrt {5-{sqrt {5+{sqrt {5+{sqrt {5-{sqrt}}}}+{{{sqrt {5-{sqrt}}}}}+{{{sqrt {5-{sqrt}}}}}+{{{sqrt}}}}}}+{{{sqrt {5-}}}}}}}}};==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	Vierkantswortel van 5, Gauss-som	5 {displaystyle {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 criptstyle \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}}}. $\scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	Som[k=0 tot 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 ) {\gamma ({tfrac {1}{4}}}) $\Gamma ({\tfrac {1}{4}})$	4 ( 1 4 ) ! = ( - 3 4 ) ! {\frac {1}{4}} rechts}!={\frac {3}{4}} rechts}! $4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	4(1/4)!	T	A068466	[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]
0.18785964246206712024851793405427323	MRB constant, Marvin Ray Burns	C M R B {\displaystyle C_{_{MRB}}} $C_{_{MRB}}$	∑ n = 1 ∞ ( - 1 ) n ( n 1 / n - 1 ) = - 1 1 + 2 2 - 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}}. $\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots$	Som[n=1 tot ∞]{(-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-constante	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 {{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 tot ∞]{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 functie	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 }{{{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}}}=}} $\prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}=$ ( 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 tot ∞]{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 constante	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}}{{{{{n=0}}^{{{{{{{n}infty}}}.1)}=e^{{{frac {1}{8}}-{{frac {1}{2}}{{{n=0}^{{frac {1}{n+1}}}}{{{k=0}^{n}{n}{{n}}{{{n}}{{{n}}{n}}{{n}}{n}}{n}{n}}{n}}{n}}{n}}{n}}{n}}{n}{n}}{n}}{n}{n}}}. $e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	e^(1/2-zeta´{-1})	T	A074962	[1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...]
7.38905609893065022723042746057500781	Schwarzschild kegelconstante	e 2 {displaystyle e^{2}} $e^{2}$	∑ n = 0 ∞ 2 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!}}+{frac {2^{4}}{4!}}. $\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots$	Som[n=0 tot ∞]{2^n/n!}	T	A072334	[7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...] = [7,2,(1,1,n,4*n+6,n+2)], n = 3, 6, 9, enz.
1.01494160640965362502120255427452028	Gieseking constant	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}}}{frac {1{n=0}^{{infty}}}+{sum _{n=1}^{infty}}}{frac {1}{(3n+2)^{2}}}+{infty}}.\sum _{n=0}^{infty }{{frac {1}{(3n+2)^{2}}}+sum _{n=1}^{infty }{frac {1}{(3n+1)^{2}}}}) =}. ${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ 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}}}{4}}{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}}}}{{{{frac {1}{10^{2}}}}}}}}... $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)$ .		T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2.62205755429211981046483958989111941	Lemniscata constant	ϖ {\displaystyle {\varpi }} ${\varpi }$	π G = 4 2 π ( 1 4 ! ) 2 {displaystyle pi, {G}=4{sqrt {tfrac {2}{\pi }}},({{{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-constante	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 s c h - g e o m e t r i s c h e m e a a n {artikel 4} {Agm:¦; rekenkundig-geometrisch;gemiddelde}{{{frac {1}{{mathrm {agm} (1,{kwart {2}})}}={{frac {4{kwart {2}},({tfrac {1}{4}!)^{2}}{{3/2}}}}}} ${\underset {Agm:\;Arithmetic-geometric\;mean}{{\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}}}$	(4 sqrt(2)(1/4!)^2)/pi^(3/2)	T	A014549	[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]
1.01734306198444913971451792979092052	Zeta(6)	ζ ( 6 ) {\displaystyle \zeta (6)} $\zeta (6)$	π 6 945 = ∏ n = 1 ∞ 1 1 - p n - 6 p n : p r i m o = 1 1 - 2 - 6 ⋅ 1 1 - 3 - 6 ⋅ 1 1 - 5 - 6 . ... {displaystyle {frac {pi ^{6}}{945}}=prod _{n=1}^{infty }{underset {p_{n}:\primo}}{frac {1}{{1-p_{n}}^{-6}}}}={frac {1}{1{-}2^{-6}}}{frac {1}{1{-}3^{-6}}{{frac {1}{1{-}5^{-6}}}...} ${\frac {\pi ^{6}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}...$	Prod[n=1 tot ∞] {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 ) {\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 ) ( 1 - 1 3 2 ) ( 1 - 1 5 2 ) ... {{displaystyle} {{frac {6}{{pi ^{2}}}{=}prod _{n=0}^{\infty }{{underset {p_{n}:\primo}}{{{p_{n}}^{2}}}}}}{=}textstyle \left(1{-}{frac {1}{p_{n}}^{2}}}}}}}}{=}textstyle \left(1{-}{{frac {1}{3^{2}}}}}}}}{{{-}{{frac {1}{5^{2}}}}}}}}}}. ${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)\dots$	Prod{n=1 tot ∞} (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	De verhouding van een vierkant en omgeschreven of ingeschreven cirkels	π 2 2 {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)^{{frac {n-1}{2}}{2n+1}}={{{frac {1}{1}}+{{frac {1}{3}}-{frac {1}{5}}-{frac {1}{7}}+{frac {1}{9}}+{{frac {1}{11}}-{{frac}}... $\sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots$	som[n=1 tot ∞]{(-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-constante	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 tot ∞] {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	Vierkantswortel van het getal e	e {displaystyle}}} ${\sqrt {e}}$	∑ n = 0 ∞ 1 2 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!}}={{frac {1}{(2n)!!}}={{frac {1}{1}{1}}+{{frac {1}{2}}+{{frac {1}{8}}+{frac {1}{48}}+{cdots}}. $\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots$	som[n=0 tot ∞]{1/(2^n n!)}	T	A019774	[1;1,1,1,5,1,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] = [1;1,(1,1,4p+1)], p∈ℕ
i	Denkbeeldig getal	i {displaystyle {i}} ${i}$	- 1 = ln ( - 1 ) π e i π = - 1 {displaystyle {sqrt {-1}}={frac {ln(-1)}{{{pi }}qquad \mathrm {e} ^{i,\pi }=-1} ${\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1$	wortel(-1)	C
262537412640768743.999999999999250073	Constante van Hermite-Ramanujan	R {Displaystyle {R}} ${R}$	e π 163 {Displaystyle e^pi {163}}}}}. $e^{\pi {\sqrt {163}}}$	e^(π sqrt(163))	T	A060295	[262537412640768743;1,1333462407511,1,8,1,1,5,...]
4.81047738096535165547303566670383313	John constant	γ {displaystyle \gamma} $\gamma$	i i = i - i = i 1 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 2 + 1 3 - 1 4 + 1 5 - ... {\displaystyle {\frac {{ln(2)}}={\frac {sum _{n=0}^{\infty }{{frac {4(-1)^{n}}{2n+1}}}{{sum _{n=1}^{\infty }{{{frac {(-1)^{n+1}}{n}}}}={\frac {4}{1}}}{-}{{frac {4}{3}}{+}{{frac {4}{5}}{-}{frac {4}{7}}{+}{{frac {4}{9}}- puntjes}}{{{frac {1}{1}}{-}{frac {1}{2}}{+}{frac {1}{3}}{-}{frac {1}{4}{+}{frac {1}{5}}- puntjes}}} ${\frac {\pi }{ln(2)}}={\frac {\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}{-}{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-\dots }{{\frac {1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}-\dots }}$	π/ln(2)	T	A163973	[4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...]
0.76159415595576488811945828260479359	Hyperbolische tangens (1)	t h 1 {displaystyle th,1} $th\,1$	e - 1 e e + 1 e = e 2 - 1 e 2 + 1 {displaystyle {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	Vervolg Fractieconstante	C C F {\displaystyle {C}_{CF}} ${C}_{CF}$	J 1 ( 2 ) J 0 ( 2 ) F u n c t i e J k ( ) B e s s e l = ∑ n = 0 ∞ n ! n ! ∑ n = 0 ∞ 1 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 {Functie}{\frac {J_{1}(2)}{J_{0}(2)}}}}={frac {sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}} {som \limits _{n=0}^{{infty }{frac {1}{n!n!}}}}={{frac {0}{1}}+{frac {1}{1}}+{frac {2}{4}}+{frac {3}{36}}+{frac {4}{576}}+{frac {1}{1}{1}}}+{frac {1}{1}{1}}}+{frac {1}{4}}+{frac {1}{36}}+{frac {1}{576}}}+{frac {1}{576}}}}}. ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(som {n=0 tot inf} n/(n!n!)) /(som {n=0 tot inf} 1/(n!n!))		A052119	[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] = [0;(p+1)], p∈ℕ
0.36787944117144232159552377016146086	Inverse constante van Napier	1 e {\frac {1}{e}}}. ${\frac {1}{e}}$	∑ n = 0 ∞ ( - 1 ) 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 }. $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots$	som[n=2 tot ∞]{(-1)^n/n!}	T	A068985	[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,1,10,1,1,12,...] = [0;2,1,(1,2p,1)], p∈ℕ
2.71828182845904523536028747135266250	Constante Napier	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}}+{{frac {1}{2!}}+{{frac {1}{3!}+{{frac {1}{4!}+{{frac {1}{5!}}+{cdots}. $\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots$	Som[n=0 tot ∞]{1/n!}	T	A001113	[2;1,2,1,1,4,1,1,6,1,1,8,1,1,1,10,1,1,12,1,...] = [2;(1,2p,1)], p∈ℕ
0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i	Factorial van i	i ! . $i\,!$	Γ ( 1 + i ) = i Γ ( i ) {\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	Oneindig Tetratie van i	∞ i {{\infty }i} ${}^{\infty }i$	lim n → ∞ n i = lim n → ∞ i i ⋅ ⋅ i ⏟ n {\displaystyle \lim _{nto \infty }{}^{n}i==lim _{nto \infty }{i^{{{n}i^^{n}}. _{n}} $\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	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	Module van Oneindig Tetratie van i	\| ∞ i \| {\displaystyle \|{{\infty }i\|}} $\|{}^{\infty }i\|$	lim n → ∞ \| n i \| = \| lim n → ∞ i ⋅ ⋅ i ⏟ n \| {{nisplaystyle {n} tot en met {n}i}rechts==left\|lim _{n{n} tot en met {n} {n}i}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^...)		A212479	[0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...]
0.26149721284764278375542683860869585	Constante Meissel-Mertens	M {Displaystyle M} $M$	lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) {\displaystyle \lim _{n\rechts \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: priemgetallen			A077761	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]
1.9287800...	Constante Wright	ω {\displaystyle \omega} $\omega$	⌊ 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle ^{2^{2^{{2^cdot ^{2^{omega }}}}}}} $\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor$ = primos: {\displaystyle \quad } $\quad$ $\left\lfloor 2^{\omega }\right\rfloor$ ⌊ 2 ω ⌋ {{Pe_230A↩ 2 ω ⌋ {{Pe_230A↩ 2 ω ⌋ {{Pe_230A↩ 2 ω ⌋ {{Pe_230A↩ 2 ω ⌋ {{Pe_230A↩ 2 ω ↪Pe_2^{omega }}}} $\left\lfloor 2^{2^{\omega }}\right\rfloor$ =13, ⌊ 2 2 2 ω ⌋ {\displaystyle \leftlfloor 2^{2^{\omega }}}rightrfloor } $\left\lfloor 2^{2^{2^{\omega }}}\right\rfloor$ =16381, ... {displaystyle stippen} $\dots$			A086238	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
0.37395581361920228805472805434641641	Artin constant	C A r t i n {{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	Feigenbaum-constante 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 _{nto \infty }{frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}} }qquad \scriptstyle x{n_{n+2}-x_{n+1}}}. $\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ 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-constante α	α {displaystyle \alpha } $\alpha$	lim n → ∞ d n d n + 1 {displaystyle \lim _{nto \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	Zeshoekige Madelung Constant ₂	H 2 ( 2 ) {\displaystyle H_{2}(2)} $H_{2}(2)$	π ln ( 3 ) 3 {{playstyle \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 ) {\beta (3)}. $\beta (3)$	π 3 32 = ∑ n = 1 ∞ - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 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}}{+}}. ${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\dots$	Som[n=1 tot ∞]{(-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 constante₂ = Σ inverse twin primes	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-constante₄ = Σ inverse van tweelingpriem	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,\2,\4,\6:\tfrac {1}{5}+{{{tfrac {1}{7}}+{{{tfrac {1}{11}}+{{{tfrac {1}{13}}}}}}}+{{tfrac {1}{11}}+{{{{tfrac {1}{13}}+{{tfrac {1}{17}}+{{{tfrac {1}{19}}}}}}}}}}}+{{{{tfrac {1}{19}}}}}}) + punten}. ${\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22.4591577183610454734271522045437350	pi^e	π e {{e}} $\pi ^{e}$	π e {{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, constante van Archimedes	π {displaystyle \pi } $\pi$	lim n → ∞ 2 n 2 - 2 + 2 + ⋯ + 2 ⏟ n {\displaystyle \lim _{nto \infty } },2^{n} {\sqrt {2-{{sqrt {2+{sqrt {2}}}}}}}} _{n}} $\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}$	Som[n=0 tot ∞]{(-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}} $e^{-e}$ ... Ondergrens van Tetratie		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 {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	Constante Bernstein	β {\displaystyle \beta } $\beta$	1 2 π {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 en Richmond	Q {Displaystyle Q}	∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 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)\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 tot ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Inverse van Pi, Ramanujan	1 π {\frac {1}{\pi}}} ${\frac {1}{\pi }}$	2 2 9801 ∑ n = 0 ∞ ( 4 n ) ! ( 1103 + 26390 n ) ( n ! ) 4 396 4 n {{displaystyle {frac {2{{sqrt {2}}}{9801}}{sum _{n=0}^{{infty }{{frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}} ${\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}$		T	A049541	[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...]
0.47494937998792065033250463632798297	Weierstraß constant	W W E {\displaystyle W_{_{WE}}} $W_{_{WE}}$	e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {displaystyle {e^{frac {{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-constante	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}}-{frac {125}{24}}}. $W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots$	som[n=1 tot ∞]{(-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	Het getal van Euler	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}}}. $-\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}$	som[n=1 tot ∞]\|sum[k=0 tot ∞]{((-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-reeks	π 3 3 {frac {pi}{3{sqrt {3}}}}} ${\frac {\pi }{3{\sqrt {3}}}}$	∑ n = 1 ∞ 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 + ⋯ {{displaystyle \sum _{n=1}^{{infty }{{frac {1}{n{2n \choose n}}}=1-{frac {1}{2}}+{frac {1}{4}-{frac {1}{5}}+{frac {1}{7}}-{frac {1}{8}}+cdots } } $\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$	Som[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 {frac {2}{{pi}}} ${\frac {2}{\pi }}$	2 2 ⋅ 2 + 2 2 ⋅ 2 + 2 2 ⋯ {\displaystyle {\frac {sqrt {2}}{2}}{2}}cdot {\frac {{sqrt {2+{sqrt {2}}}}{2}}}}cdot {\frac {{sqrt {2+{sqrt {2+{sqrt {2}}}}}}{2}}}cdots } ${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
0.66016181584686957392781211001455577	Tweelingpriemconstante	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 tot ∞]{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	Limietconstante van Laplace	λ {displaystyle \lambda } $\lambda$				A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0.69314718055994530941723212145817657	Logaritme van 2	L n ( 2 ) {Ln(2)}. $Ln(2)$	∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ⋯ {{displaystyle \sum _{n=1}^{{infty }{{{frac {(- 1)^{n+1}{n}}={{{frac {1}{1}}}-{{frac {1}{2}}+{{frac {1}{3}}}+{{frac {1}{1}}}}.1)^{n+1}}{n}}={{frac {1}{1}}-{frac {1}{2}}+{frac {1}{3}}-{frac {1}{4}}+{{frac {1}{5}}-{cdots}}. $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots$	Som[n=1 tot ∞]{(-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 = 1 - 1 2 2 + 1 3 3 - 1 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}}}+{frac {1}{5^{5}}}... $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots$	Som[ -(-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 ) {\beta (1)}. $\beta (1)$	π 4 = ∑ n = 0 ∞ ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - ⋯ {\displaystyle {{4}}=sum _{n=0}^{infty }{{frac {(- 1)^{n}{2n+1}}={frac {1}{1}{1}}}-{{frac {1}{3}}+{frac {1}{5}}}}.1)^{n}}{2n+1}}={{frac {1}{1}}-{{frac {1}{3}}+{frac {1}{5}}-{frac {1}{7}}+{{frac {1}{9}}-{cdots}}. ${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	Som[n=0 tot ∞]{(-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	Reizende verkoper Nielsen-Ramanujan	ζ ( 2 ) 2 {\frac {\zeta (2)}{2}} ${\frac {\zeta (2)}{2}}$	π 2 12 = ∑ n = 1 ∞ ( - 1 ) n + 1 n 2 = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\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}}}{n^{2}}}{n^{2}}}. ${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots$	Som[n=1 tot ∞]{((-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	Catalaanse constante	C {Displaystyle C} $C$	∑ n = 0 ∞ ( - 1 ) n ( 2 n + 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 {1}{1^{2}}}-{{frac {1+1}}{3^{2}}}}.1)^{n}}{(2n+1)^{2}}={{{frac {1}{1^{2}}}-{{frac {1}{3^{2}}+{{frac {1}{5^{2}}}-{{frac {1}{7^{2}}}+{cdots }. $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots$	Som[n=0 tot ∞]{(-1)^n/(2n+1)^2}	I	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1.05946309435929526456182529494634170	Verhouding van de afstand tussen halve tonen	2 12 {displaystyle {sqrt[{12}]{2}}} ${\sqrt[{12}]{2}}$	2 12 {displaystyle {sqrt[{12}]{2}}} ${\sqrt[{12}]{2}}$	2^(1/12)	I	A010774	[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]
1,.08232323371113819151600369654116790	Zeta(04)	ζ 4 {{ displaystyle \zeta {4}} $\zeta {4}$	π 4 90 = ∑ n = 1 ∞ 1 n 4 = 1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 + 1 5 4 + ... {\displaystyle {\frac {{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 }. ${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+\dots$	Som[n=1 tot ∞]{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 the Wayback Machine constant	C V i {Displaystyle C_{Vi}} $C_{Vi}$	lim n → ∞ \| a n \| 1 n {\displaystyle \lim _{nto \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 constant	ζ ( 3 ) {\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 ^{\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}}}+{displaystyle}},\!} $\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots \,\!$	Som[n=1 tot ∞]{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	Constante Favard	3 4 ζ ( 2 ) {\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 } ${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\dots$	som[n=1 tot ∞]{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	Derdemachtswortel van 2, constante 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 = 1 + 1 2 2 + 1 3 3 + 1 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}}}+{{frac {1}{frac {1}{6^{6}}}. $\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}=1+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}+\dots$	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	Plastic nummer	ρ {{ displaystyle \rho} $\rho$	1 + 1 + 1 + 1 + ⋯ 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	Vierkantswortel van 2, constante van Pythagoras	2 {displaystyle {2}}} ${\sqrt {2}}$	∏ n = 1 ∞ 1 + ( - 1 ) n + 1 2 n - 1 = ( 1 + 1 1 ) ( 1 - 1 3 ) ( 1 + 1 5 ) . . . {\displaystyle \prod _{n=1}^{\infty }1+{{frac {(-1)^{n+1}}{2n-1}}}=1{+}{frac {1}{1}{1}} rechts)\left(1{-}{frac {1}{3}} rechts)\left(1{+}{frac {1}{5}}} rechts)...} $\prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\left(1{+}{\frac {1}{1}}\right)\left(1{-}{\frac {1}{3}}\right)\left(1{+}{\frac {1}{5}}\right)...$	prod[n=1 tot ∞]{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-getal	e 1 e {{frac {1}{e}}}} $e^{\frac {1}{e}}$	e 1 / e {{1/e}} $e^{1/e}$ ... Bovengrens van Tetratie			A073229	[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
1.53960071783900203869106341467188655	Lieb's Vierkante ijsconstante	W 2 D {\displaystyle W_{2D}} $W_{2D}$	lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 {displaystyle \lim _{nto \infty }(f(n))^{n^{-2}}={frac {4}{3}} rechts)^{frac {3}{2}}}. $\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}$	(4/3)^(3/2)	I	A118273	[1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...]
1.57079632679489661923132169163975144	Product Wallis	π / 2 {{³'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 ⋯ {{{n=1}^{{infty }}left({{4n^{2}}{4n^{2}-1}} rechts)={{frac {2}{1}}}}{frac {2}{3}}}}{frac {4}{3}}}}{frac {4}{5}}}{frac {6}{5}}}}{frac {6}{7}}}{frac {8}{7}}}{frac {8}{9}}}. $\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$		T	A019669	[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1...]
1.60669515241529176378330152319092458	Erdős-Borwein constante	E B {Displaystyle E_{,B}} $E_{\,B}$	∑ n = 1 ∞ 1 2 n - 1 = 1 1 + 1 3 + 1 7 + 1 15 + ⋯ {{{n=1}^{infty }{{frac {1}{2^{n}-1}}={{frac {1}{1}}+{{frac {1}{3}}+{{frac {1}{7}}+{frac {1}{15}}}+{cdots ║. $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!$	som[n=1 tot ∞]{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, gulden snede	φ {\displaystyle \varphi } $\varphi$	1 + 5 2 = 1 + 1 + 1 + ⋯ {{displaystyle {1+{\sqrt {5}}}{2}}={{{\sqrt {1+{{\sqrt {1+{{\sqrt {1+{\sqrt {1+{\sqrt}}}}{2}}}. ${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(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 (ζ,2)}. $\zeta (\,2)$	π 2 6 = ∑ n = 1 ∞ 1 n 2 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 + ⋯ {displaystyle {{{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 }. ${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	Som[n=1 tot ∞]{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	Kwadratische terugkeerconstante van Somos	σ {displaystyle \sigma} $\sigma$	1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {displaystyle {1{sqrt {2{sqrt {3{cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}{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 constant	3 {displaystyle {3}}} ${\sqrt {3}}$	3 {displaystyle {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 {1+{{{{\sqrt {2+{{{\sqrt {3+{{\dots} }}}}}}}}} ${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$			A072449	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
1.77245385090551602729816748334114518	Constante Carlson-Levin	Γ ( 1 2 ) {\displaystyle \Gamma ({tfrac {1}{2}})} $\Gamma ({\tfrac {1}{2}})$	π = ( - 1 2 ) ! {displaystyle {sqrt {pi}}={{{frac {1}{2}}} links(-{{frac {1}{2}} rechts)}! ${\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!$	wortel (pi)	T	A002161	[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]
2.29558714939263807403429804918949038	Universele parabolische constante	P 2 {Displaystyle P_{,2}} $P_{\,2}$	ln ( 1 + 2 ) + 2 {\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	Bronsnummer	σ R r {{³'sigma'}}. $\sigma _{\,Rr}$	${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(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-constante₂	2 ln γ {{displaystyle 2\ln \gamma}. $2\,\ln \,\gamma$	π 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	vierkantswortel van 2 pi	2 π {{"displaystyle" {2}} ${\sqrt {2\pi }}$	2 π = lim n → ∞ n ! e n n n n {displaystyle {2pi }}=lim _{nto \infty }{frac {n!;e^{n}}{n^{n}{nqrt {n}}}}} ${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}$	wortel (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-constante	G G S {Displaystyle G_{_{\,GS}}} $G_{_{\,GS}}$	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 constant	K 0 {Displaystyle K_{,0}} $K_{\,0}$	∏ n = 1 ∞ [ 1 + 1 n ( n + 2 ) ] ln n / ln 2 {{displaystyle _{n=1}^{{infty } } ^{1+{1 over n(n+2)}} ^{ln n/{ln 2}}}. $\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	prod[n=1 tot ∞]{(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	Constante van Khinchin-Lévy	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	Reciproke Fibonacci constante	Ψ {Psi}. $\Psi$	∑ n = 1 ∞ 1 F n = 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}}+{{frac {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	Wortel van 2 e pi	2 e π {{ displaystyle}} ${\sqrt {2e\pi }}$	2 e π {{ displaystyle}} ${\sqrt {2e\pi }}$	sqrt(2e pi)	T	A019633	[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]
6.58088599101792097085154240388648649	Constante Froda	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 kwadraat	π 2 {{2}} $\pi ^{2}$	6 ∑ n = 1 ∞ 1 n 2 = 6 1 2 + 6 2 2 + 6 3 2 + 6 4 2 + ⋯ {{{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 Som[n=1 tot ∞]{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 constant	e π {Displaystyle e} $e^{\pi }$	∑ n = 0 ∞ π n n ! = π 1 1 + π 2 2 ! + π 3 3 ! + π 4 4 ! + ⋯ {\displaystyle \sum _{n=0}^{\infty }{{frac {{n}}{n!}}={{frac {{1}}{1}}+{{frac {{2}}{2!}}+{{frac {{3}}{3!}}+{{frac {{4}}{4!}}+{cdots }. $\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	Som[n=0 tot ∞]{(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]

Gerelateerde pagina's

Constante functie
Lijst van wiskundige symbolen

Boeken

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

Daniel Zwillinger (2012). Standaard wiskundige tabellen en formules. Imperial College Press. ISBN 978-1-4398-3548-7.

Eric W. Weisstein (2003). CRC Beknopte encyclopedie van de wiskunde. Chapman & Hall/CRC. ISBN 1-58488-347-2.

Lloyd Kilford (2008). Modulaire vormen, een klassieke en computationele inleiding. Imperial College Press. ISBN 978-1-84816-213-6.

Online bibliografie

Online encyclopedie van gehele reeksen (OEIS)
Simon Plouffe, Tabellen van Constanten
De pagina met getallen, wiskundige constanten en algoritmen van Xavier Gourdon en Pascal Sebah
MathConstants

Vragen en antwoorden

V: Wat is een wiskundige constante?

A: Een wiskundige constante is een getal dat een speciale betekenis heeft voor berekeningen.

V: Wat is een voorbeeld van een wiskundige constante?

A: Een voorbeeld van een wiskundige constante is ً, die de verhouding weergeeft tussen de omtrek van een cirkel en zijn diameter.

V: Is de waarde van ً altijd hetzelfde?

A: Ja, de waarde van ً is voor elke cirkel altijd gelijk.

V: Zijn wiskundige constanten integraal?

A: Nee, wiskundige constanten zijn meestal reële, niet-integraal getallen.

V: Waar komen wiskundige constanten vandaan?

A: Wiskundige constanten komen niet zoals natuurkundige constanten voort uit fysische metingen.