Constante mathematic

Un constante mathematic es un quantitate que non varia.

Contento

1 Constantes importante
2 Structura del tabulas
3 Lista de constantes
4 references
5 Ligamines externe
6 Creditos y recognocimientos
7 Colaborations

Constantes importante[modificar | modificar fonte]

Structura del tabulas[modificar | modificar fonte]

Valor numeric del constante, generalmente con 35 decimales.
Nomine: Con lo que habitualmente illo es cognoscite.
Symbolo: de identification, in multe casos es un littera grec.
LaTeX: Formula in le formato LaTeX.
Formula in texto: Formula in formato texto, por poter copiar e pegar in programmas como Mathematica.
OEIS: Ligamine al fundation: On-Line Encyclopedia of Integer Sequences (OEIS), ubi on pote consultar le constantes con plus detalios.
Fraction continue: In le formato simple [Parte integre; frac1, frac2, frac3, ...] (en negrita si es periodic)
Tipo:
- R - Numero racional
- I - Numero irracional
- T - Numero trascendental
- ? - desconocido

Lista de constantes[modificar | modificar fonte]

Le ultime constantes subidas, se encuentran al principio del tablula.

Puede selectionar le ordinate de la lista, pulsando en el nomine, valor, OEIS, etc.

Valor	Nomine	Symbolo	LaTeX	Formula in texto	Tipo	OEIS	Fraction continue
3,24697960371746706105000976800847962	Constante Silver de Tutte–Beraha	$\varsigma$	$2+2 \cos(2\pi/7)= \textstyle 2+\frac{2+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}{1+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}$	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	Constante París	$C_{Pa}$	$\prod_{n=2}^\infty \frac{2 \varphi}{\varphi+ \varphi_n}\; , \varphi= {Fi}$		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 nested radical R₅	$R_{5}$	$\scriptstyle \sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}}\;=\textstyle\frac{2+\sqrt{5}+\sqrt{15-6\sqrt{5}}}{2}$	(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	Raíz de 5, Suma de Gauss	$\sqrt{5}$	$\scriptstyle \forall \, n=5, \displaystyle \sum_{k=0}^{n-1} e^{\frac{2 k^2 \pi i}{n}} = 1 + e^\frac{2 \pi i} {5} + e^\frac{8 \pi i} {5} + e^\frac{18 \pi i} {5} + e^\frac{32 \pi i} {5}$	Sum[k=0 to 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)	$\Gamma(\tfrac14)$	$4 \left(\frac{1}{4}\right)! = \left(-\frac{3}{4}\right)!$	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	Constante MRB de Marvin Ray Burns	$C_{_{MRB}}$	$\sum_{n=1}^{\infty} ({-}1)^n (n^{1/n}{-}1) = - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \sqrt[4]{4}\,...$	Sum[n=1 to ∞]{(-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	Constante de Kepler–Bouwkamp	${\rho}$	$\prod_{n=3}^\infty \cos\left(\frac\pi n\right) = \cos\left(\frac\pi 3\right) \cos\left(\frac\pi 4\right) \cos\left(\frac\pi 5\right) ...$	prod[n=3 to ∞]{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) función G-Barnes	$e^{\gamma}$	$\prod_{n=1}^\infty \frac{e^{\frac{1}{n}}}{1+\tfrac1n} = \prod_{n=0}^\infty \left(\prod_{k=0}^n (k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac{1}{n+1}} =$ $\textstyle \left ( \frac{2}{1} \right )^{1/2} \left (\frac{2^2}{1 \cdot 3} \right )^{1/3} \left (\frac{2^3 \cdot 4}{1 \cdot 3^3} \right )^{1/4} \left (\frac{2^4 \cdot 4^4}{1 \cdot 3^6 \cdot 5} \right )^{1/5}...$	Prod[n=1 to ∞]{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	Constante de Glaisher–Kinkelin	${A}$	$e^{\frac{1}{12}-\zeta^{\prime}(-1)} = e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^{\infty} \frac{1}{n+1} \sum\limits_{k=0}^{n} \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)}$	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	Constante conica de Schwarzschild	$e^2$	$\sum_{n = 0}^\infty \frac{2^n}{n!} = 1+2+\frac{2^2}{2!}+\frac{2^3}{3!}+\frac{2^4}{4!}+\frac{2^5}{5!}+...$	Sum[n=0 to ∞]{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, etc.
1,01494160640965362502120255427452028	Constante Gieseking	${G_{Gi}}$	$\frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)=$ $\textstyle \frac{3\sqrt{3}}{4} \left( 1 - \frac{1}{2^2} + \frac{1}{4^2}-\frac{1}{5^2}+\frac{1}{7^2}-\frac{1}{8^2}+\frac{1}{10^2} \pm ... \right)$ .		T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2,62205755429211981046483958989111941	Constante Lemniscata	${\varpi}$	$\pi \, {G} = 4 \sqrt{\tfrac2\pi} \,(\tfrac14 !)^2$	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	Constante de Gauss	${G}$	$\underset{ agm:\; Media \;aritm\acute{e}tica-geom\acute{e}trica} {\frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{4 \sqrt{2} \,(\tfrac14 !)^2}{\pi ^{3/2}}}$	(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,...]
0,0078749969978123844	Constante de Chaitin	${\Omega}$	$\sum_{p \in P} 2^{-\|p\|} \overset {p: \; {Programa \; que \;se \; para}} \underset{ { P:\; Conjunto \; de \; todos \; los \; programas \; que \; se \; paran.}} {\scriptstyle [p]:\; Tama\tilde{n}o \;del\;programa }$		?	A100264	[0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1]
1,01734306198444913971451792979092052	Constante Zeta(6)	$\zeta(6)$	$\frac{\pi^6}{945} = \prod_{n=1}^\infty \underset{p_{n}: \, {primo}}\frac{1}{{1-p_n}^{-6}} = \frac{1}{1{-}2^{-6}}{\cdot}\frac{1}{1{-}3^{-6}}{\cdot}\frac{1}{1{-}5^{-6}} ...$	Prod[n=1 to ∞] {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	$\frac{1}{\zeta(2)}$	$\frac{6}{\pi^2} {=} \prod_{n = 0}^\infty \underset{p_{n}: \, {primo}}{\left(1- \frac{1}{{p_n}^2}\right)}{=}\textstyle \left(1{-}\frac{1}{2^2}\right)\left(1{-}\frac{1}{3^2}\right)\left(1{-}\frac{1}{5^2}\right)...$	Prod{n=1 to ∞} (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	Razón entre un cuadrado y las círcunferencias ins.o circunscrita	$\frac{\pi}{2\sqrt 2}$	$\sum_{n = 1}^\infty \frac{(-1)^{\lfloor \frac{n-1}{2}\rfloor}}{2n+1} = \frac{1}{1} + \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \frac{1}{9} + \frac{1}{11} - ...$	sum[n=1 to ∞]{(-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	Constante Fransen–Robinson	${F}$	$\int_{0}^\infty \frac{1}{\Gamma(x)}\, dx. = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, dx$	N[int[0 to ∞] {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	Raiz cuadrada del numero e	$\sqrt e$	$\sum_{n = 0}^\infty \frac{1}{2^n n!} = \sum_{n = 0}^\infty \frac{1}{(2n)!!} = \frac{1}{1}+\frac{1}{2}+\frac{1}{8}+\frac{1}{48}+\cdots$	sum[n=0 to ∞]{1/(2^n n!)}	T	A019774	[1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] = [1;1,(1,1,4p+1)], p∈ℕ
i	Numero imaginario	${i}$	$\sqrt{-1} = \frac{\ln(-1)}{\pi} \qquad\qquad \mathrm{e}^{i\,\pi} = -1$	sqrt(-1)	C
262537412640768743,999999999999250073	Constante de Hermite-Ramanujan	${R}$	$e^{\pi\sqrt{163}}$	e^(π sqrt(163))	T	A060295	[262537412640768743;1,1333462407511,1,8,1,1,5,...]
4,81047738096535165547303566670383313	Constante de John	$\gamma$	$\sqrt[i]{i} = i^{-i} = i^{\frac{1}{i}} = (i^i)^{-1} = e^{\frac{\pi}{2}}$	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	$\alpha$	$\frac{\pi}{ln(2)} = \frac{\sum_{n = 0}^\infty \frac{4(-1)^n}{2n+1}} {\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}} = \frac{\frac{4}{1} {-} \frac{4}{3} {+} \frac{4}{5} {-} \frac{4}{7} {+} \frac{4}{9} - ...} {\frac{1}{1}{-}\frac{1}{2}{+}\frac{1}{3}{-}\frac{1}{4}{+}\frac{1}{5}-...}$	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	Tangente hiperbólica de 1	$th \, 1$	$\frac{e-\frac{1}{e}}{e+\frac{1}{e}} = \frac{e^2-1}{e^2+1}$	(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	Constante de fraccion continua	${C}_{CF}$	$\underset{J_{k}() {Bessel}}\underset{{Funci\acute{o}n}}\frac{J_1(2)}{J_0(2)} = \frac{ \sum\limits_{n = 0}^{\infty} \frac{n}{n!n!}} {{ \sum\limits_{n = 0}^{\infty} \frac{1}{n!n!}}} = \frac{\frac{0}{1}+\frac{1}{1}+\frac{2}{4}+\frac{3}{36}+\frac{4}{576}+...} {\frac{1}{1}+\frac{1}{1}+\frac{1}{4}+\frac{1}{36}+\frac{1}{576}+...}$	(sum {n=0 to inf} n/(n!n!)) /(sum {n=0 to 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	Inverso del Numero neperian	1/e	$\sum_{n = 0}^\infty \frac{(-1)^n}{n!} = \frac{1}{0!} - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} +\cdots$	sum[n=2 to ∞]{(-1)^n/n!}	T	A068985	[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [0;2,1,(1,2p,1)], p∈ℕ
2,71828182845904523536028747135266250	Numero neperian, constante de Euler	e	$\sum_{n = 0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \cdots$	Sum[n=0 to ∞]{1/n!}	T	A001113	[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [2;(1,2p,1)], p∈ℕ
0,49801566811835604271369111746219809 - 0,15494982830181068512495513048388 i	Factorial de i	i !	$\Gamma (1+i) = i \Gamma (i)$	Gamma(1+i)		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	Tetración infinite de i	${}^\infty i$	$\lim_{n \to \infty} {}^n i = \lim_{n \to \infty} \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n$	i^i^i^...		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	Modulo de la Tetración infinite de i	$\| {}^\infty i \|$	$\lim_{n \to \infty} \left \| {}^n i \right \| =\left \| \lim_{n \to \infty} \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n \right \|$	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 de Meissel-Mertens	M	$\lim_{n \rightarrow \infty } \left( \sum_{p \leq n} \frac{1}{p} - \ln(\ln(n)) \right)$ ..... p: primos			A077761	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]
1,9287800...	Constante de Wright	ω	$\left \lfloor 2^{2^{2^{\cdot^{\cdot^{2^{\omega}}}}}} \right \rfloor$ = primos: $\quad$ $\left\lfloor 2^\omega\right\rfloor$ =3, $\left\lfloor 2^{2^\omega} \right\rfloor$ =13, $\left\lfloor 2^{2^{2^\omega}} \right\rfloor$ =16381, $\dots$			A086238	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
0,37395581361920228805472805434641641	Constante de Artin	C_Artin	$\prod_{n=1}^{\infty} \left(1-\frac{1}{p_n(p_n-1)}\right)$ ...... 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	Constante δ de Feigenbaum	δ	$\lim_{n \to \infty}\frac {x_{n+1}-x_n}{x_{n+2}-x_{n+1}}$ ...... $x \in (3,8284; 3,8495)$ $x_{n+1}=ax_n(1-x_n)$ ...o... $x_{n+1}=a\sin(x_n)$		T	A006890	[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
2,50290787509589282228390287321821578	Constante α de Feigenbaum	α	$\lim_{n \to \infty}\frac {d_n}{d_{n+1}}$		T	A006891	[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
5,97798681217834912266905331933922774	Constante hexagonal Madelung ₂	H₂(2)	$\pi \ln(3) \sqrt 3$	Pi Log[3]Sqrt[3]	T	A086055	[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]
0,83462684167407318628142973279904680	Constante de Gauss	G_Ga	$\frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{[\Gamma(\tfrac14)]^2}{(2 \pi)^{3/2}}$	Γ[1/4]]^2/(2Pi^{3/2}Sqrt(2)	T	A014549	[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]
0,96894614625936938048363484584691860	Constante Beta(3)	β(3)	$\frac{\pi^3}{32} = \sum_{n=1}^\infty\frac{-1^{n+1}}{(-1+2n)^3} = \frac{1}{1^3}-\frac{1}{3^3} + \frac{1}{5^3} - \frac{1}{7^3} + \cdots\,\!$	Sum[n=1 to ∞]{(-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	Constante de Brun ₂ = Σ inv. numeros primos gemelos	B ₂	$\textstyle \sum (\frac1{p}+\frac1{p+2}) = (\frac1{3} + \frac1{5}) + (\tfrac1{5} + \tfrac1{7}) + (\tfrac1{11} + \tfrac1{13}) + \ldots$ p, p+2 primos			A065421	[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
0,870588379975	Constante de Brun ₄ = Σ inv. numeros primos gemelos	B ₄	$\left(\tfrac1{5} + \tfrac1{7} + \tfrac1{11} + \tfrac1{13}\right) + \left(\tfrac1{11} + \tfrac1{13} + \tfrac1{17} + \tfrac1{19}\right)+ \ldots$ p, p+2, p+4, p+6 primos			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22,4591577183610454734271522045437350	pi^e	π^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	Numero π, constante de Arquimedes	π	$\lim_{n\to \infty }\, 2^{n} \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\text{...} +\sqrt{2}}}}}_n$	Sum[n=0 to ∞]{(-1)^n 4/(2n+1)}	T	A000796	[3;7,15,1,292,1,1,1,2,1,3,1,14,...]
0,06598803584531253707679018759684642		e^-e	$e^{-e}$ ... Limite inferior de Tetración		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	iⁱ	$e^ \frac{-\pi}{2}$	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 de Bernstein	β	$\frac {1}{2\sqrt {\pi}}$		T	A073001	[0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…]
0,28878809508660242127889972192923078	Flajolet and Richmond	Q	$\prod_{n=1}^{\infty} \left(1 - \frac{1}{2^n}\right) = \left(1-\frac{1}{2^1}\right) \left(1-\frac{1}{2^2} \right)\left(1-\frac{1}{2^3} \right)\cdots$	prod[n=1 to ∞]{1-1/2^n}		A048651
0,31830988618379067153776752674502872	Inverso de Pi, Ramanujan	1/π	$\frac{2\sqrt{2}}{9801} \sum^\infty_{n=0} \frac{(4n)!(1103+26390n)}{(n!)^4 396^{4n}}$		T	A049541	[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...]
0,47494937998792065033250463632798297	Constante de Weierstrass	W_WE	$\frac{e^{\frac{\pi}{8}}\sqrt{\pi}}{4*2^{3/4} {(\frac {1}{4}!)^2}}$	(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	Constante Omega	Ω=W(1)	$\sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!} = 1 - 1 + \frac{3}{2} - \frac{8}{3} + \frac{125}{24} - \cdots$	sum[n=1 to ∞]{(-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	Constante de Euler-Mascheroni	γ	$-\psi(1) = \sum_{n=1}^\infty \sum_{k=0}^\infty \frac{(-1)^k}{2^n+k}$	sum[n=1 to ∞]\|sum[k=0 to ∞]{((-1)^k)/(2^n+k)}	?	A001620	[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,...]
0,60459978807807261686469275254738524	Serie de Dirichlet	π/(3√3)	$\frac{\pi}{3 \sqrt 3} = \sum_{n = 1}^\infty \frac{1}{n{2n \choose n}} = 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{5} + \frac{1}{7} - \frac{1}{8} + \cdots$	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 por, François Viète	2/π	$\frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
0,66016181584686957392781211001455577	Constante de los primos gemelos	C₂	$\prod_{p=3}^\infty \frac{p(p-2)}{(p-1)^2}$	prod[p=3 to ∞]{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	Constante límite de Laplace	λ				A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0,69314718055994530941723212145817657	Logaritmo natural de 2	Ln(2)	$\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} = \frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\cdots$	Sum[n=1 to ∞]{(-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 Dream ₁ J.Bernoulli	I₁	$\sum_{n = 1}^\infty \frac{(-1)^{n+1}}{n^n} = 1 - \frac{1}{2^2} + \frac{1}{3^3} - \frac{1}{4^4} + \frac{1}{5^5} - \frac{1}{6^6}+ \cdots$	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 β(1)	π/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 to ∞]{(-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	Traveling Salesman, Nielsen-Ramanujan	ζ(2)/2	$\frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} - \frac{1}{2^2} + \frac{1}{3^2} - \frac{1}{4^2} + \frac{1}{5^2} -\cdots$	Sum[n=1 to ∞]{((-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	Constante de Catalan	C	$\sum_{n = 0}^\infty \frac{(-1)^n}{(2n+1)^2} = \frac{1}{1^2}-\frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\cdots$	Sum[n=0 to ∞]{(-1)^n/(2n+1)^2}	I	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1,05946309435929526456182529494634170	Constante entre semitonos de la escala musical	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	Constante Zeta(04)	ζ(4)	$\frac{\pi^4}{90} = \sum_{n=1}^\infty\frac{{1}}{n^4} = \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \frac{1}{4^4} + \frac{1}{5^4} + \frac{1}{6^4} +\cdots$	Sum[n=1 to ∞]{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 ...	Constante de Viswanath	C_Vi	$\lim_{n \to \infty}\|a_n\|^\frac{1}{n}$			A078416	[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]
1,20205690315959428539973816151144999	Constante de Apery	ζ(3)	$\sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots\,\!$	Sum[n=1 to ∞]{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(¾)	$\left(-1+\frac{3}{4}\right)!$	(-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 de Favard	¾ ζ(2)	$\frac{\pi^2}{8} = \sum_{n = 0}^\infty \frac{1}{(2n-1)^2} = \frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots$	sum[n=1 to ∞]{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	Radice cubica de dos, constante Delian	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 Dream ₂ J.Bernoulli	I₂	$\sum_{n = 1}^\infty \frac{1}{n^n} = 1 + \frac{1}{2^2} + \frac{1}{3^3} + \frac{1}{4^4} + \frac{1}{5^5} + \frac{1}{6^6} + \frac{1}{7^7} + \cdots$	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	Numero plástico	ρ	$\sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \cdots}}}}$		I	A060006	[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...]
1,41421356237309504880168872420969808	Radice cuadrada de 2, constante de Pitagoras	√2	$\prod_{n=1}^\infty 1+\frac{(-1)^{n+1}}{2n-1} = \left(1+\frac{1}{1}\right) \left(1-\frac{1}{3} \right)\left(1+\frac{1}{5} \right)\cdots$	prod[n=1 to ∞]{1+(-1)^(n+1)/(2n-1)}	I	A002193	[1;(2),...]
1,44466786100976613365833910859643022	Numero de Steiner	e^1/e	$e^{1/e}$ ... Límite superior de Tetración			A073229	[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
1,53960071783900203869106341467188655	Constante Square Ice de Lieb	W_2D	$\lim_{n \to \infty}(f(n))^{n^{-2}}=\left(\frac{4}{3}\right)^\frac{3}{2}$	(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	Producto de Wallis	π/2	$\prod_{n=1}^{\infty} (\frac{4n^2}{4n^2 - 1}) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots$		T	A019669	[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1...]
1,60669515241529176378330152319092458	Constante de Erdős–Borwein	E_B	$\sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} + \frac{1}{3} + \frac{1}{7} + \frac{1}{15} + \cdots\,\!$	sum[n=1 to ∞]{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	Fi, Número áureo	Φ	$\frac{1 + \sqrt{5}}{2} = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}}$	(1+5^(1/2))/2	I	A001622	[0;(1),...]
1,64493406684822643647241516664602519	Función Zeta (2) de Riemann	ζ(2)	$\frac{\pi^2}{6} = \sum_{n=1}^\infty\frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots$	Sum[n=1 to ∞]{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	Recurrencia cuadrática de Somos	σ	$\sqrt {1 \sqrt {2 \sqrt{3 \cdots}}} = 1^{1/2} ; 2^{1/4} ; 3^{1/8} \cdots$		T	A065481	[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
1,73205080756887729352744634150587237	Constante de Theodorus	√3	$\sqrt{3}$	3^(1/2)	I	A002194	[1;(1,2),...]
1,75793275661800453270881963821813852	Numero de Kasner	K	$\sqrt{1 + \sqrt{2 + \sqrt{3 + \sqrt{4 + \cdots}}}}$			A072449	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
1,77245385090551602729816748334114518	Constante de Carlson-Levin	Γ(1/2)	$\sqrt{\pi} = \left(-\frac{1}{2}\right)!$	sqrt (pi)	T	A002161	[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]
2,23606797749978969640917366873127624	Radice quadrate de 5	√5	$\sqrt{5}$	5^(1/2)	I	A002163	[2;(4),...]
2,29558714939263807403429804918949038	Constante universal parabolic	P₂	$\ln(1 + \sqrt2) + \sqrt2$	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	Numero de bronce	σ_Br	$\frac {3+\sqrt{13}}{2} = 1+ \sqrt{3+\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}}$	(3+sqrt 13)/2	I	A098316	[3;(3),...]
2,37313822083125090564344595189447424	Constante de Levy ₂	2lnγ	$\frac{\pi^2}{6ln(2)}$	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	Radice quadrate de 2 pi	(2π)^1/2	$\sqrt{2 \pi}$	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	Constante de Gelfond-Schneider	G_GS	$2^{\sqrt{2}}$	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	Constante de Khintchin	K₀	$\prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\ln n/\ln 2}$	prod[n=1 to ∞]{(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 de Khinchin-Lévy	γ	$e^{\pi^2/(12\ln2)}$	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	Constante de los inversos de Fibonacci	ψ	$\sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots$			A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4,13273135412249293846939188429985264	Raíz de 2 e pi	√(2eπ)	$\sqrt{2e \pi}$	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 de Froda	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 al Cuadrado	π²	$6 \sum_{n=1}^\infty \frac{1}{n^2} = \frac{6}{1^2} + \frac{6}{2^2} + \frac{6}{3^2} + \frac{6}{4^2}+ \cdots$	6 Sum[n=1 to ∞]{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	Constante de Gelfond	e^π	$\sum_{n=0}^\infty \frac{\pi^{n}}{n!} = \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2!} + \frac{\pi^{3}}{3!} + \frac{\pi^{4}}{4!}+ \cdots$	Sum[n=0 to ∞]{(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]