Constantă matematică | număr, care are o semnificație specială pentru calcule

O constantă matematică este un număr care are o semnificație specială pentru calcule. De exemplu, constanta π (pronunțată "plăcintă") reprezintă raportul dintre circumferința unui cerc și diametrul său. Această valoare este întotdeauna aceeași pentru orice cerc. O constantă matematică este adesea un număr real, neintegral, de interes.

Spre deosebire de constantele fizice, constantele matematice nu provin din măsurători fizice.

Constante matematice cheie

Tabelul următor conține câteva constante matematice importante:

Nume	Simbol	Valoare	Adică
Pi, constanta lui Arhimede sau numărul lui Ludoph	π	≈3.141592653589793	Un număr transcendental care reprezintă raportul dintre lungimea circumferinței unui cerc și diametrul acestuia. Este, de asemenea, aria cercului unitar.
E, constanta lui Napier sau numărul lui Euler (pronunțat "oilers")	e	≈2.718281828459045	Un număr transcendental care reprezintă baza logaritmilor naturali, numit uneori "număr natural".
Raportul de aur	φ	5 + 1 2 ≈ 1.618 {\displaystyle {\frac {{\sqrt {5}}+1}{2}}}\aprox 1.618} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	Este valoarea unei valori mai mari împărțită la o valoare mai mică, dacă aceasta este egală cu valoarea sumei valorilor împărțită la valoarea mai mare.
Rădăcina pătrată a lui 2, constanta lui Pitagora	2 {\displaystyle {\sqrt {2}}}} ${\sqrt {2}}$	≈ 1.414 {\displaystyle \aprox. 1.414} $\approx 1.414$	Un număr irațional care reprezintă lungimea diagonalei unui pătrat cu laturile de lungime 1. Acest număr nu poate fi scris sub formă de fracție.

Constante și serii

Tabelul următor conține o listă de constante și serii în matematică, cu următoarele coloane:

Valoare: Valoarea numerică a constantei.
LaTeX: Formule sau serii în format TeX.
Formula: Pentru utilizare în programe precum Mathematica sau Wolfram Alpha.
OEIS: Legătură către On-Line Encyclopedia of Integer Sequences (OEIS), unde sunt disponibile constantele cu mai multe detalii.
Fracțiune continuată: În forma simplă [la număr întreg; frac1, frac2, frac3, ...] (între paranteze dacă este periodic)
Tip:

R - Număr rațional
I - Număr irațional
T - Număr transcendental
C - Număr complex

Rețineți că lista poate fi ordonată în mod corespunzător făcând clic pe titlul antetului din partea superioară a tabelului.

Valoare	Nume	Simbol	LaTeX	Formula	Tip	OEIS	Fracțiune continuă
3.24697960371746706105000976800847962	Argint, Tutte-Beraha constant	ς {\displaystyle \varsigma } $\varsigma$	2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 2 + 7 + 7 7 + 7 7 + 7 7 + ⋯ 3 3 3 1 + 7 + 7 + 7 7 + 7 7 + ⋯ 3 3 3 3 {\displaystyle 2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}} $2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}$	2+2 cos(2Pi/7)	T	A116425	[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]
1.09864196439415648573466891734359621	Paris constant	C P a {\displaystyle C_{Pa}} $C_{Pa}$	∏ n = 2 ∞ 2 φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}}} $\prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}$		I	A105415	[1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...]
2.74723827493230433305746518613420282	Ramanujan radical imbricate R₅	R 5 {\displaystyle R_{5}} $R_{5}$	5 + 5 + 5 + 5 - 5 + 5 + 5 + 5 + 5 - ⋯ = 2 + 5 + 5 + 15 - 6 5 5 2 {\displaystyle \scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}} $\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(2+sqrt(5)+sqrt(15-6 sqrt(5)))/2	I		[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]
2.23606797749978969640917366873127624	Rădăcina pătrată a lui 5, suma Gauss	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 \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 la 4]{e^(2k^2 pi i/5)}	I	A002163	[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] = [2;(4),...]
3.62560990822190831193068515586767200	Gamma(1/4)	Γ ( 1 4 ) {\displaystyle \Gamma ({\tfrac {1}{4}})} $\Gamma ({\tfrac {1}{4}})$	4 ( 1 4 ) ! = ( - 3 4 ) ! {\displaystyle 4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!} $4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	4(1/4)!	T	A068466	[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]
0.18785964246206712024851793405427323	MRB constant, 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 + 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 la ∞]{(-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	Constanta Kepler-Bouwkamp	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}}\dreapta)=\cos \left({\frac {\pi }{3}}\dreapta)\cos \left({\frac {\pi }{4}}\dreapta)\cos \left({\frac {\pi }{5}}\dreapta)\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 la ∞]{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) Funcția G-Barnes	e γ {\displaystyle e^{\gamma }}} $e^{\gamma }$	∏ n = 1 ∞ e 1 n 1 + 1 n = ∏ n = 0 ∞ ( ∏ k = 0 ( k + 1 ) ( - 1 ) k + 1 ( n k ) ) 1 n + 1 = {\displaystyle \prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \alege 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 până la ∞]{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	Constanta Glaisher-Kinkelin	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 \sum \limits _{k=0}^{n}\left(-1\dreapta)^{k}{{\binom {n}{k}}}\left(k+1\dreapta)^{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	Constanta conică Schwarzschild	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 la ∞]{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,n,4*n+6,n+2)], n = 3, 6, 9, etc.
1.01494160640965362502120255427452028	Constanta Gieseking	G G i {\displaystyle {G_{Gi}}} ${G_{Gi}}$	3 3 4 ( 1 - ∑ n = 0 ∞ 1 ( 3 n + 2 ) 2 + ∑ n = 1 ∞ 1 ( 3 n + 1 ) 2 ) = {\displaystyle {\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=} ${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ 3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± ... ) {\displaystyle \textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}}\pm \dots \right)} $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)$ .		T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2.62205755429211981046483958989111941	Lemniscata constantă	ϖ {\displaystyle {\varpi }} ${\varpi }$	π G = 4 2 π ( 1 4 ! ) 2 {\displaystyle \pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}}}\,({\tfrac {1}{4}}!)^{2}}} $\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,({\tfrac {1}{4}}!)^{2}$	4 sqrt(2/pi) (1/4!)^2	T	A062539	[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]
0.83462684167407318628142973279904680	Constanta Gauss	G {\displaystyle {G}} ${G}$	1 a g m ( 1 , 2 ) = 4 2 ( 1 4 ! ) 2 π 3 / 2 A g m : A r i t h m e t i c - g e o m e t r i c m e a n {\displaystyle {\underset {Agm:\;Arithmetic-geometric\;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 {1}{{1{1-p_{n}}^{-6}}}}={\frac {1}{1{-{-}2^{-6}}}{\cdot }{\frac {1}{1{-{-}3^{-6}}}{\cdot }{\frac {1}{1{-{-}5^{-6}}}...} ${\frac {\pi ^{6}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}...$	Prod[n=1 la ∞] {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 {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 {\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 până la ∞} (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	Raportul dintre un pătrat și cercurile circumscrise sau înscrise	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 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 - ... {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}{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 la ∞]{(-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	Constanta Fransén-Robinson	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 la ∞] {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	Rădăcina pătrată a numărului 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 2 + 1 8 + 1 48 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}{1}}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots } $\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots$	sum[n=0 la ∞]{1/(2^n n!)}	T	A019774	[1;1,1,1,1,5,1,1,1,9,1,1,1,13,1,1,1,17,1,1,1,21,1,1,1,...] = [1;1,(1,1,4p+1)], p∈ℕ
i	Număr imaginar	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	Constanta Hermite-Ramanujan	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 constant	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 2 + 1 3 - 1 4 + 1 5 - ... {\displaystyle {\frac {\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 {{\frac {4}{1}}}{-}{{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-puncte }{{\frac {1}{1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}}-puncte }}} ${\frac {\pi }{ln(2)}}={\frac {\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}{-}{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-\dots }{{\frac {1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}-\dots }}$	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	Tangentă hiperbolică (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+{\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;1,3,3,5,7,9,11,13,15,17,19,21,23,25,27,...] = [0;(2p+1)], p∈ℕ
0.69777465796400798200679059255175260	Constantă de fracție continuă	C C C F {\displaystyle {C}_{CF}} ${C}_{CF}$	J 1 ( 2 ) J 0 ( 2 ) F u n c ț i o n e 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 {Funcție}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}{1}}+{\frac {2}{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 }}} ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(suma {n=0 la inf} n/(n!n!)) /(suma {n=0 până la inf} 1/(n!n!))		A052119	[0;1;1,2,3,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] = [0;(p+1)], p∈ℕ
0.36787944117144232159552377016146086	Constanta inversă a lui Napier	1 e {\displaystyle {\frac {1}{e}}}} ${\frac {1}{e}}$	∑ n = 0 ∞ ( - 1 ) n n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! + ... {\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 până la ∞]{(-1)^n/n!}	T	A068985	[0;2,1,1,1,2,1,1,1,4,1,1,1,6,1,1,1,8,1,1,1,10,1,1,1,12,...] = [0;2,1,(1,2p,1)], p∈ℕ
2.71828182845904523536028747135266250	Napier constant	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 } $\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots$	Suma[n=0 până la ∞]{1/n!}	T	A001113	[2;1;1,2,1,1,1,4,1,1,1,6,1,1,1,8,1,1,1,10,1,1,1,12,1,...] = [2;(1,2p,1)], p∈ℕ
0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i	Factorial de 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	Infinit Tetrație de i	∞ i {\displaystyle {}^{\infty }i} ${}^{\infty }i$	lim n → ∞ n i = lim n → ∞ i i i ⋅ ⋅ i ⏟ n {\displaystyle \lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}} $\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	i^i^i^i^...	C	A077589 A077590	[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...] + [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i
0.56755516330695782538461314419245334	Modulul de Infinit Tetrația lui i	\| ∞ i \| {\displaystyle \|{}^{\infty }i\|} $\|{}^{\infty }i\|$	lim n → ∞ \| n i \| n i \| = \| lim n → ∞ i i 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} {\n}Dreapta\|} $\lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right\|$	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	Constanta Meissel-Mertens	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: prime			A077761	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]
1.9287800...	Constanta Wright	ω {\displaystyle \omega } $\omega$	⌊ 2 2 2 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor } $\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor$ = primos: {\displaystyle \quad } $\quad$ ⌊ 2 ω ⌋ {\displaystyle \left\lfloor 2^{\omega }\right\rfloor } $\left\lfloor 2^{\omega }\right\rfloor$ =3, ⌊ 2 2 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^{\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	Constanta Artin	C A r t i n {\displaystyle C_{Artin}} $C_{Artin}$	∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \prod _{n=1}^{\infty }\left(1-{{\frac {1}{p_{n}(p_{n}-1)}}}\right)} $\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)$ ...... p_n : primo		T	A005596	[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]
4.66920160910299067185320382046620161	Constanta Feigenbaum δ	δ {\displaystyle {\delta }} ${\delta }$	lim n → ∞ x n + 1 - x n x n + 2 - x n + 1 x ∈ ( 3 , 8284 ; 3 , 8495 ) {\displaystyle \lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)} $\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ x n + 1 = a x n ( 1 - x n ) o x n + 1 = a sin ( x n ) {\displaystyle \scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {o}\quad x_{n+1}=\,a\sin(x_{n})} $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {o}\quad x_{n+1}=\,a\sin(x_{n})$		T	A006890	[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
2.50290787509589282228390287321821578	Constanta Feigenbaum α	α {\displaystyle \alpha } $\alpha$	lim n → ∞ d n d n d n + 1 {\displaystyle \lim _{n\to \infty }{\frac {d_{n}}}{d_{n+1}}}} $\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$		T	A006891	[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
5.97798681217834912266905331933922774	Hexagonal Madelung Constant ₂	H 2 ( 2 ) {\displaystyle H_{2}(2)} $H_{2}(2)$	π ln ( 3 ) 3 {\displaystyle \pi \ln(3){\sqrt {3}}}}} $\pi \ln(3){\sqrt {3}}$	Pi Log[3]Sqrt[3]	T	A086055	[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]
0.96894614625936938048363484584691860	Beta(3)	β ( 3 ) {\displaystyle \beta (3)} $\beta (3)$	π 3 32 = ∑ n = 1 ∞ - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + ... {\displaystyle {\frac {\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 la ∞]{(-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 constant₂ = Σ prime gemene inverse	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	Constanta Brun₄ = Σ inversa primului geamăn	B 4 {\displaystyle B_{\\,4}} $B_{\,4}$	( 1 5 + 1 7 + 1 11 + 1 13 ) p , p + 2 , p + 4 , p + 6 : p r i m e s + ( 1 11 + 1 13 + 1 17 + 1 19 ) + ... {\displaystyle {\underset {p,\,p+2,\,p+4,\,\,p+6:\,{primes}}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots } ${\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22.4591577183610454734271522045437350	pi^e	π e {\displaystyle \pi ^{e}} $\pi ^{e}$	π e {\displaystyle \pi ^{e}} $\pi ^{e}$	pi^e		A059850	[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]
3.14159265358979323846264338327950288	Pi, constanta lui Arhimede	π {\displaystyle \pi } $\pi$	lim n → ∞ 2 n 2 n 2 - 2 - 2 + 2 + ⋯ + 2 ⏟ n {\displaystyle \lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}} $\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}$	Sum[n=0 până la ∞]{(-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}} $e^{-e}$ ... Limita inferioară a tetrației		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	Constanta Bernstein	β {\displaystyle \beta } $\beta$	1 2 π {\displaystyle {\frac {1}{2{\sqrt {\pi }}}}} ${\frac {1}{2{\sqrt {\pi }}}}$		T	A073001	[0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…]
0.28878809508660242127889972192923078	Flajolet și Richmond	Q {\displaystyle Q}	∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 2 2 ) ( 1 - 1 2 2 ) ( 1 - 1 2 3 ) ... {\displaystyle \prod _{n=1}^{\infty }\left(1-{{\frac {1}{2^{n}}}\dreapta)=\left(1{-}{\frac {1}{2^{1}}}\dreapta)\left(1{-}{\frac {1}{2^{2}}}\dreapta)\left(1{-}{\frac {1}{2^{3}}}\dreapta)\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 la ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Inversa lui Pi, Ramanujan	1 π {\displaystyle {\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 constant	W W E {\displaystyle W_{_{WE}} $W_{_{WE}}$	e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {\displaystyle {\frac {e^{\frac {\pi }{8}}}{\sqrt {\pi }}}{42^{3/4}{{({\frac {1}{4}}!)^{2}}}}} ${\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{42^{3/4}{({\frac {1}{4}}!)^{2}}}}$	(E^(Pi/8) Sqrt[Pi])/(4 2^(3/4) (1/4)!^2)	T	A094692	[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,...]
0.56714329040978387299996866221035555	Constanta Omega	Ω {\displaystyle \Omega } $\Omega$	W ( 1 ) = ∑ n = 1 ∞ ( - n ) n - 1 n ! = 1 - 1 + 3 2 - 8 3 + 125 24 - ... {\displaystyle W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}}{+}{\frac {125}{24}}}-\dots } $W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots$	sum[n=1 la ∞]{(-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	Numărul lui 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}}}} $-\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}$	sum[n=1 până la ∞]\|sum[k=0 până la ∞]{((-1)^k)/(2^n+k)}	?	A001620	[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,...]
0.60459978807807261686469275254738524	Seria Dirichlet	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 \alege 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 {2}{\pi }}}} ${\frac {2}{\pi }}$	2 2 2 ⋅ 2 + 2 2 2 ⋅ 2 + 2 + 2 + 2 2 ⋯ {\displaystyle {\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2+{\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	Constanta primelor gemene	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 la ∞]{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	Constanta limită Laplace	λ {\displaystyle \lambda } $\lambda$				A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0.69314718055994530941723212145817657	Logaritm de 2	L n ( 2 ) {\displaystyle Ln(2)} $Ln(2)$	∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {(- - -1)^{n+1}}}{n}}={{\frac {1}{1}{1}}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots$	Sum[n=1 la ∞]{(-1)^(n+1)/n}	T	A002162	[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...]
0.78343051071213440705926438652697546	Visul celui de-al doilea an de liceu₁ 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 - 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}}}+\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 până la ∞]{(-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	Vânzătorul ambulant 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 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\displaystyle {\frac {\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}}}}-puncte } ${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots$	Sum[n=1 la ∞]{((-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	Constanta catalană	C {\displaystyle C} $C$	∑ n = 0 ∞ ( - 1 ) n ( 2 n + 1 ) 2 = 1 1 1 2 - 1 3 2 + 1 5 2 - 1 7 2 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{\frac {(- - -1)^{n}}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots$	Sum[n=0 la ∞]{(-1)^n/(2n+1)^2}	I	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1.05946309435929526456182529494634170	Raportul dintre distanța dintre semitonuri	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 5 4 + ... {\displaystyle {\frac {\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 la ∞]{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 \| 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 constant	ζ ( 3 ) {\displaystyle \zeta (3)} $\zeta (3)$	∑ n = 1 ∞ 1 n 3 = 1 1 1 3 + 1 2 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={{\frac {1}{1}{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 la ∞]{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	Constanta Favard	3 4 ζ ( 2 ) {\displaystyle {\tfrac {3}{4}}}\zeta (2)} ${\tfrac {3}{4}}\zeta (2)$	π 2 8 = ∑ n = 0 ∞ 1 ( 2 n - 1 ) 2 = 1 1 1 2 + 1 3 2 + 1 5 2 + 1 7 2 + ... {\displaystyle {\frac {\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{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 la ∞]{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	Rădăcină cubică de 2, constantă 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	Visul celui de-al doilea an de liceu₂ J.Bernoulli	I 2 {\displaystyle I_{2}} $I_{2}$	∑ n = 1 ∞ 1 n 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}}}+\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	Număr de plastic	ρ {\displaystyle \rho } $\rho$	1 + 1 + 1 + 1 + 1 + ⋯ 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	Rădăcina pătrată a lui 2, constanta lui Pitagora	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}}\dreapta)\left(1{-}{\frac {1}{3}}\dreapta)\left(1{+}{\frac {1}{5}}\dreapta)...} $\prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\left(1{+}{\frac {1}{1}}\right)\left(1{-}{\frac {1}{3}}\right)\left(1{+}{\frac {1}{5}}\right)...$	prod[n=1 la ∞]{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	Numărul Steiner	e 1 e {\displaystyle e^{\frac {1}{e}}} $e^{\frac {1}{e}}$	e 1 / e {\displaystyle e^{1/e}} $e^{1/e}$ ... Limita superioară a tetrației			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 constant	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	Produsul Wallis	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 5 ⋅ 6 5 ⋅ 6 7 ⋅ 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}}\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	Constanta Erdős-Borwein	E B {\displaystyle E_{\,B}} $E_{\,B}$	∑ n = 1 ∞ 1 2 n - 1 = 1 1 1 + 1 3 + 1 3 + 1 7 + 1 15 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{2}{2^{n}-1}}}={\frac {1}{1}{1}}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!} $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!$	sum[n=1 la ∞]{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, raportul de aur	φ {\displaystyle \varphi } $\varphi$	1 + 5 2 = 1 + 1 + 1 + 1 + 1 + 1 + ⋯ {\displaystyle {\frac {1+{\sqrt {5}}}{2}}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+{\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 + 1 3 2 + 1 4 2 + ⋯ {\displaystyle {\frac {\pi ^{2}}{6}}}=\suma _{{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 la ∞]{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	Constanta de recurență pătratică a lui Somos	σ {\displaystyle \sigma } $\sigma$	1 2 3 ⋯ = 1 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots } ${\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots$		T	A065481	[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
1.73205080756887729352744634150587237	Constanta Theodorus	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	Numărul Kasner	R {\displaystyle R} $R$	1 + 2 + 3 + 3 + 4 + ⋯ {\displaystyle {\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}} ${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$			A072449	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
1.77245385090551602729816748334114518	Constanta Carlson-Levin	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	Constanta parabolică universală	P 2 {\displaystyle P_{\,2}} $P_{\,2}$	ln ( 1 + 2 ) + 2 {\displaystyle \lnn(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	Număr de bronz	σ R 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+{\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	Constanta Lévy₂	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	rădăcina pătrată a 2 pi	2 π {\displaystyle {\sqrt {2\pi }}} ${\sqrt {2\pi }}$	2 π = lim n → ∞ n ! e n n n n n n {\displaystyle {\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}}{n^{n}{\sqrt {n}}}}} ${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}$	sqrt (2*pi)	T	A019727	[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]
2.66514414269022518865029724987313985	Constanta Gelfond-Schneider	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 constant	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 \1 peste 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 până la ∞]{(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	Constanta 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	Constanta reciprocă Fibonacci	Ψ {\displaystyle \Psi } $\Psi$	∑ n = 1 ∞ 1 F n = 1 1 1 + 1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1 13 + ⋯ {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={{\frac {1}{1}{1}}+{\frac {1}{1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots } $\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$			A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4.13273135412249293846939188429985264	Rădăcina lui 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	Constanta 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 la pătrat	π 2 {\displaystyle \pi ^{2}} $\pi ^{2}$	6 ∑ n = 1 ∞ 1 n 2 = 6 1 2 + 6 2 2 + 6 2 2 + 6 3 2 + 6 4 2 + ⋯ {\displaystyle 6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{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 până la ∞]{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^{\pi}} $e^{\pi }$	∑ n = 0 ∞ π n n n ! = π 1 1 1 + π 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 până la ∞]{(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]

Pagini conexe

Funcție constantă
Lista de simboluri matematice

Cărți

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

Daniel Zwillinger (2012). Tabele și formule matematice standard. 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.

Bibliografie online

Enciclopedia on-line a secvențelor de numere întregi (OEIS)
Simon Plouffe, Tabele de constante
Pagina de numere, constante matematice și algoritmi a lui Xavier Gourdon și Pascal Sebah
MathConstants

Întrebări și răspunsuri

Î: Ce este o constantă matematică?

R: O constantă matematică este un număr care are o semnificație specială pentru calcule.

Î: Care este un exemplu de constantă matematică?

R: Un exemplu de constantă matematică este ً, care reprezintă raportul dintre circumferința unui cerc și diametrul său.

Î: Valoarea lui ً este întotdeauna aceeași?

R: Da, valoarea lui ً este întotdeauna aceeași pentru orice cerc.

Î: Sunt constantele matematice numere integrale?

R: Nu, constantele matematice sunt, de obicei, numere reale, neintegrale.

Î: De unde provin constantele matematice?

R: Constantele matematice nu provin din măsurători fizice, așa cum fac constantele fizice.