AMIGOS PARA SIEMPRE: Algoritmos

Algoritmos de precisión arbitraria

Constantes y funciones matemáticas

La estructura de la tabla es la siguiente:

Valor numérico de la constante y enlace a MathWorld o a OEIS Wiki.
LaTeX: Fórmula o serie en el formato TeX.
Fórmula: Para utilizar en Wolfram Alpha. Si en los cálculos, ∞ demora mucho tiempo, puede cambiarse por 20000, para obtener un resultado aproximado.
OEIS: On-Line Encyclopedia of Integer Sequences.
Fracción continua: En el formato simple [Parte entera; frac1, frac2, frac3, ...] , suprarrayada si es periódica.
Año: Del descubrimiento de la constante, o datos del autor.
Formato web: Valor de la constante, en formato adecuado para los buscadores web.
N.º: Tipo de Número
- R - Racional
- I - Irracional
- A - Algebraico
- T - Trascendental
- C - Complejo

(La tabla se puede ordenar ascendente o descendente, por cualquiera de los campos, sin más que pulsar en los títulos del encabezado).

Constantes y funciones matemáticas
Valor	Nombre	Gráfico	Símbolo	LaTeX	Fórmula	N.º	OEIS	Fracción continua	Año	Formato web
0,07077 60393 11528 80353 -0,68400 03894 37932 129 i ^{Ow 1}	Constante MKB ¹ · ² · ³		$M_I$	$\lim_{n\rightarrow \infty} \int_{1}^{2n} (-1)^x ~ \sqrt[x]{x} ~ dx = \int_{1}^{2n} e^{i \pi x} ~ x^{1/x} ~ dx$	lim_(2n->∞) int[1 to 2n] {exp(iPix)*x^(1/x) dx}	C	A255727 A255728	[0;14,7,1,2,1,23,2,1,8,16,1,1,3,1,26,1,6,1,1, ...] - [0;1,2,6,13,41,112,1,25,1,1,1,1,3,13,2,1, ...] i	2009	0.07077603931152880353952802183028200 -0.68400038943793212918274445999266 i
3,05940 74053 42576 14453 ^{Mw 1}^{Ow 2}	Constante Doble factorial		${C_{_{n!!}}}$	$\sum_{n=0}^{\infty} \frac{1}{n!!} = \sqrt{e} \left[\frac {1}{\sqrt{2}}+\gamma(\tfrac12 ,\tfrac12)\right]$	Sum[n=0 to ∞]{1/n!!}		A143280	[3;16,1,4,1,66,10,1,1,1,1,2,5,1,2,1,1,1,1,1,2,...]		3.05940740534257614453947549923327861
0,62481 05338 43826 58687 + 1,30024 25902 20120 419 i	Fracción continua generalizada de i		${{F}_{CG}}_{(i)}$	$\textstyle i{+}\frac i{i+\frac i{i+\frac i{i+\frac i{i+\frac i{i+\frac i{i+i{/...}}}}}}} = \sqrt{\frac{\sqrt{17}-1}{8}} + i \left(\tfrac12 {+} \sqrt{\frac{2}{\sqrt{17}-1}}\right)$	i+i/(i+i/(i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/(i+i/(i+i/( ...)))))))))))))))))))))	C A	A156590 A156548	[i;1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,..] = [0;1,i]		0.62481053384382658687960444744285144 + 1.30024259022012041915890982074952 i
0,91893 85332 04672 74178 ^{Mw 2}	Fórmula de Raabe ⁴		${\zeta'(0)}$	$\int\limits_a^{a+1}\log\Gamma(t)\,\mathrm dt = \tfrac12\log2\pi + a\log a - a,\quad a \ge 0$	integral_a^(a+1) {log(Gamma(x))+a-a log(a)} dx		A075700	[0;1,11,2,1,36,1,1,3,3,5,3,1,18,2,1,1,2,2,1,1,...]		0.91893853320467274178032973640561763
0,42215 77331 15826 62702 ^{Mw 3}	Volumen delTetraedro de Reuleaux ⁵		${V_{_{R}}}$	$\frac{s^3}{12}(3\sqrt2 - 49 \, \pi + 162 \, \arctan\sqrt2)$	(3Sqrt[2] - 49Pi + 162*ArcTan[Sqrt[2]])/12		A102888	[0;2,2,1,2,2,7,4,4,287,1,6,1,2,1,8,5,1,1,1,1, ...]		0.42215773311582662702336591662385075
1,17628 08182 59917 50654 ^{Mw 4}	Constante de Salem,conjetura de Lehmer ⁶		${\sigma_{_{10}}}$	$x^{10}+x^9-x^7-x^6-x^5-x^4-x^3+x+1$	x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1	A	A073011	[1;5,1,2,17,1,7,2,1,1,2,4,7,2,2,1,1,15,1,1, ...	1983?	1.17628081825991750654407033847403505
2,39996 32297 28653 32223 ^{Mw 5} Radianes	Ángulo áureo ⁷		${b}$	$(4-2\,\Phi)\,\pi = (3-\sqrt{5})\,\pi$ = 137.507764050037854646 ...°	(4-2Phi)Pi	T	A131988	[2;2,1,1,1087,4,4,120,2,1,1,2,1,1,7,7,2,11,...]	1907	2.39996322972865332223155550663361385
1,26408 47353 05301 11307 ^{Mw 6}	Constante de Vardi ⁸		${V_c}$	$\frac{\sqrt{3}}{\sqrt{2}}\prod_{n\ge1}\left(1+{1\over(2e_n-1)^2}\right)^{\!1/2^{n+1}}$			A076393	[1;3,1,3,1,2,5,54,7,1,2,1,2,3,15,1,2,1,1,2,1,...]	1991	1.26408473530530111307959958416466949
1,5065918849 ± 0,0000000028^{Mw 7}	Área del fractal de Mandelbrot ⁹		$\gamma$	Se conjetura que el valor exacto es: $\sqrt{6\pi -1} - e$ = 1,506591651...			A098403	[1;1,1,37,2,2,1,10,1,1,2,2,4,1,1,1,1,5,4,...]	1912	1.50659177 +/- 0.00000008
1,61111 49258 08376 736 111···111 27224 36828 ^{Mw 8} ^{^{183213 unos}}	Constante Factorial exponencial		${S_{Ef}}$	$\sum_{n=1}^{\infty} \frac{1}{n^{(n{-}1)^{\cdot^{\cdot^{\cdot^{2^1}}}}}} = 1 {+} \frac{1}{2^{1}} {+} \frac{1}{3^{2^{1}}} + \frac{1}{4^{3^{2^{1}}}} + \frac{1}{5^{4^{3^{2^{1}}}}} {+} \cdots$		T	A080219	[1; 1, 1, 1, 1, 2, 1, 808, 2, 1, 2, 1, 14,...]		1.61111492580837673611111111111111111
0,31813 15052 04764 13531 ±1,33723 57014 30689 40 i ^{Ow 3}	Punto fijo Super-logaritmo ¹⁰ · ¹¹		${-W(-1)}$	$\lim_{n\rightarrow \infty}$ $f(x) = \underbrace{\log(\log(\log(\log(\cdots\log(\log(x)))))) \,\! }\atop {\log_s \text{ anidados n veces}}$ Para un valor inicial de x distinto a 0, 1, e, e^e, e^(e^e), etc.	-W(-1) Donde W=ProductLog Lambert W function	C	A059526 A059527	[-i;1 +2i,1+i,6-i,1+2i,-7+3i,2i,2,1-2i,-1+i,-, ...]		0.31813150520476413531265425158766451 -1.33723570143068940890116214319371 i
1,09317 04591 95490 89396 ^{Mw 9}	Constante de Smarandache 1ª ¹²		${S_1}$	$\sum_{n=2}^\infty \frac1{\mu(n)!} {\color{white}....\color{black}}$ La función Kempner μ(n) se define como sigue: μ(n) es el número más pequeño por el que μ(n)! es divisible por n			A048799	[1;10,1,2,1,2,1,13,3,1,6,1,2,11,4,6,2,15,1,1,...]		1.09317045919549089396820137014520832
1,64218 84352 22121 13687 ^{Mw 10}	Constante de Lebesgue L2 ¹³		${L2}$	$\frac{1}{5} + \frac{\sqrt{25-2\sqrt{5}}}{\pi} = \frac{1}{\pi} \int_0^\pi \frac {\left\|\sin(\frac{5t}{2})\right\|} {\sin(\frac{t}{2})} \,d t$	1/5 + sqrt(25 - 2*sqrt(5))/Pi	T	A226655	[1;1,1,1,3,1,6,1,5,2,2,3,1,2,7,1,3,5,2,2,1,1,...]	1910	1.64218843522212113687362798892294034
0,82699 33431 32688 07426 ^{Mw 11}	Disk Covering ¹⁴		${C_5}$	${\frac{1}{{\sum_{n=0}^\infty \frac{1}{\binom{3n+2}{2}}}}} = \frac{3\sqrt{3}}{2\pi}$	3 Sqrt[3]/(2 Pi)	T	A086089	[0;1,4,1,3,1,1,4,1,2,2,1,1,7,1,4,4,2,1,1,1,1,...]	1939 1949	0.82699334313268807426698974746945416
1,78723 16501 82965 93301 ^{Mw 12}	Constante de Komornik–Loreti ¹⁵		${q}$	$1 = \!\sum_{n=1}^\infty \frac{t_k}{q^k} \qquad \scriptstyle \text{Raiz real de} \displaystyle\prod_{n=0}^\infty \!\left (\! 1 {-} \frac{1}{q^{2^n}} \!\right ) \! {+} \frac{q{-}2}{q{-}1}=0$ t _k = Sucesión de Thue-Morse	FindRoot[(prod[n=0 to ∞] {1-1/(x^2^n)}+ (x-2)/(x-1))= 0, {x, 1.7}, WorkingPrecision->30]	T	A055060	[1;1,3,1,2,3,188,1,12,1,1,22,33,1,10,1,1,7,...]	1998	1.78723165018296593301327489033700839
0,59017 02995 08048 11302 ^{Mw 13}	Constante de Chebyshev ¹⁶ · ¹⁷		${\lambda_{Ch}}$	$\frac{\Gamma(\tfrac14)^2}{4 \pi^{3/2}} = \frac{4 (\tfrac14 !)^2}{\pi^{3/2}}$	(Gamma(1/4)^2) /(4 pi^(3/2))		A249205	[0;1,1,2,3,1,2,41,1,6,5,124,5,2,2,1,1,6,1,2,...]		0.59017029950804811302266897027924429
0,52382 25713 89864 40645 ^{Mw 14}	Función Chi Coseno hiperbólico integral		${\operatorname{Chi()}}$	$\gamma + \int_0^x\frac{\cosh t-1}{t}\,dt$ $\scriptstyle \gamma \, \text{= Constante de Euler–Mascheroni = 0,5772156649...}$	Chi(x)		A133746	[0;1,1,9,1,172,1,7,1,11,1,1,2,1,8,1,1,1,1,1,...]		0.52382257138986440645095829438325566
0,62432 99885 43550 87099 ^{Mw 15}	Constante de Golomb–Dickman¹⁸		${\lambda}$	$\int \limits_{0}^{\infty} \underset{Para \; x>2}{\frac{f(x)}{x^2} dx} = \int \limits_{0}^{1} e^{Li(n)} dn \quad \scriptstyle \text{Li = Integral logarítmica}$	N[Int{n,0,1}[e^Li(n)],34]		A084945	[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...]	1930 y 1964	0.62432998854355087099293638310083724
0,98770 03907 36053 46013 ^{Mw 16}	Área delimitada por la rotación excéntrica del Triángulo de Reuleaux¹⁹		$\mathcal{T}_R$	$a^2 \cdot \left( 2\sqrt{3} + {\frac{\pi}{6}} - 3 \right)$ donde a= lado del cuadrado	2 sqrt(3)+pi/6-3	T	A066666	[0;1,80,3,3,2,1,1,1,4,2,2,1,1,1,8,1,2,10,1,2,...]	1914	0.98770039073605346013199991355832854
0,70444 22009 99165 59273	Constante Carefree₂²⁰		$\mathcal{C}_2$	$\underset{ p_n: \, {primo}}{\prod_{n = 1}^\infty \left(1 - \frac{1}{p_n(p_n+1)}\right)}$	N[prod[n=1 to ∞] {1 - 1/(prime(n)* (prime(n)+1))}]		A065463	[0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...]		0.70444220099916559273660335032663721
1,84775 90650 22573 51225 ^{Mw 17}	Constante camino auto-evitante en red hexagonal ²¹ · ²²		${\mu}$	$\sqrt{2 + \sqrt{2}} \; = \lim_{n \rightarrow \infty} c_n^{1/n}$ La menor raíz real de $: \; x ^ 4-4 x ^ 2 + 2=0$	sqrt(2+sqrt(2))	A	A179260	[1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...]		1.84775906502257351225636637879357657
0,19452 80494 65325 11361 ^{Mw 18}	2ª Constante Du Bois Reymond ²³		${C_2}$	$\frac{e^2-7}{2} = \int_0^\infty \left\|{\frac{d}{dt}\left(\frac{\sin t}{t}\right)^n}\right\|\,dt-1$	(e^2-7)/2	T	A062546	[0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...] = [0;2p+3], p∈ℕ		0.19452804946532511361521373028750390
2,59807 62113 53315 94029 ^{Mw 19}	Área de un hexágono de lado unitario ²⁴		$\mathcal{A}_6$	$\frac{3 \sqrt{3}}{2}\,l^2$	3 sqrt(3)/2	A	A104956	[2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] [2;1,1,2,20,2,1,1,4]		2.59807621135331594029116951225880855
1,78657 64593 65922 46345 ^{Mw 20}	Constante de Silverman ²⁵		${\mathcal{S}_{_{m}}}$	$\sum_{n = 1}^\infty \frac {1}{\phi (n)\sigma_1(n)} = \underset{ p_n: \, {primo}}{ \prod_{n = 1}^\infty \left( 1 + \sum_{k = 1}^\infty \frac {1}{p_n^{2k} - p_n^{k-1}}\right)}$ ø() = Función totien de Euler, σ₁() = Función divisor.	Sum[n=1 to ∞] {1/[EulerPhi(n) DivisorSigma(1,n)]}		A093827	[1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...]		1.78657645936592246345859047554131575
1,46099 84862 06318 35815 ^{Mw 21}	Constante cuatro-colores de Baxter ²⁶	Mapamundi Coloreado 4C	$\mathcal{C}^2$	$\prod_{n = 1}^\infty \frac{(3n-1)^2}{(3n-2)(3n)} = \frac {3}{4\pi^2} \,\Gamma \left(\frac {1}{3}\right)^3$ Γ() = Función Gamma	3×Gamma(1/3) ^3/(4 pi^2)		A224273	[1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...]	1970	1.46099848620631835815887311784605969
0,66131 70494 69622 33528 ^{Mw 22}	Constante de Feller-Tornier ²⁷		${\mathcal{C}_{_{FT}}}$	$\underset{p_n: \, {primo}}{\frac{1}{2}\prod_{n = 1}^\infty \left(1-\frac{2}{p_n^2}\right){+}\frac{1}{2}} =\frac{3}{\pi^2}\prod_{n = 1}^\infty \left(1-\frac{1}{p_n^2-1}\right){+}\frac{1}{2}$	[prod[n=1 to ∞] {1-2/prime(n)^2}] /2 + 1/2	T ?	A065493	[0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...]	1932	0.66131704946962233528976584627411853
1,92756 19754 82925 30426 ^{Mw 23}	Constante Tetranacci		$\mathcal{T}$	La mayor raíz real de $: \;\; x^4-x^3-x^2-x-1=0$	Root[x+x^-4-2=0]	A	A086088	[1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...]		1.92756197548292530426190586173662216
1,00743 47568 84279 37609 ^{Mw 24}	Constante DeVicci's Teseracto		${f_{(3,4)}}$	Arista del mayor cubo, dentro de un hipercubo unitario 4D. La menor raíz real de $: \;\; 4x^4{-}28x^3{-}7x^2{+}16x{+}16=0$	Root[4x^8-28x^6 -7x^4+16x^2+16 =0]	A	A243309	[1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...]		1.00743475688427937609825359523109914
0,15915 49430 91895 33576 ^{Mw 25}	Constante A de Plouffe ²⁸		${A}$	$\frac{1}{2 \pi}$	1/(2 pi)	T	A086201	[0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...]		0.15915494309189533576888376337251436
0,41245 40336 40107 59778 ^{Mw 26}	Constante de Thue-Morse ²⁹		$\tau$	$\sum_{n=0}^{\infty} \frac{t_n}{2^{n+1}}$ donde ${t_n}$ es la secuencia Thue–Morse y donde $\tau(x) = \sum_{n=0}^{\infty} (-1)^{t_n} \, x^n = \prod_{n=0}^{\infty} ( 1 - x^{2^n} )$		T	A014571	[0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...]		0.41245403364010759778336136825845528
0,58057 75582 04892 40229 ^{Mw 27}	Constante de Pell³⁰		${\mathcal{P}_{_{Pell}}}$	$1- \prod_{n = 0}^\infty \left(1-\frac{1}{2^{2n+1}}\right)$	N[1-prod[n=0 to ∞] {1-1/(2^(2n+1)}]	T ?	A141848	[0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...]		0.58057755820489240229004389229702574
2,20741 60991 62477 96230 ^{Mw 28}	Problema moviendo el sofá de Hammersley³¹		${S_{_{H}}}$	$\frac {\pi}{2} +\frac {2}{\pi} \,$ ¿Cuál es el área más grande de una forma, que pueda ser maniobrada en un pasillo en forma de L y tenga de ancho la unidad ?	pi/2 + 2/pi	T	A086118	[2;4,1,4,1,1,2,5,1,11,1,1,5,1,6,1,3,1,1,1,1,7,...]	1967	2.20741609916247796230685674512980889
1,15470 05383 79251 52901 ^{Mw 29}	Constante de Hermite³²		$\gamma_{_{2}}$	$\frac{2}{\sqrt{3}} = \frac{1}{\cos \, (\frac{\pi}{6})}$	2/sqrt(3)	A	1+ A246724	[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] [1;6,2]		1.15470053837925152901829756100391491
0,63092 97535 71457 43709 ^{Mw 30}	Dimensión fractal del Conjunto de Cantor ³³		$d_f(k)$	$\lim_{\varepsilon \to 0} \frac {\log N(\varepsilon)}{\log (1/\varepsilon)} = \frac{\log 2}{\log 3}$	log(2)/log(3) N[3^x=2]	T	A102525	[0;1,1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]		0.63092975357145743709952711434276085
0,17150 04931 41536 06586 ^{Mw 31}	Constante Hall-Montgomery ³⁴		${{\delta}_{_{0}}}$	$1 + \frac{\pi^2}{6} +2 \; \mathrm{Li}_2 \left(-\sqrt{e}\;\right) \quad \mathrm{Li}_2 \, \scriptstyle \text{= Integral dilogarítmica}$	1 + Pi^2/6 + 2*PolyLog[2, -Sqrt[E]]		A143301	[0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...]		0.17150049314153606586043997155521210
1,55138 75245 48320 39226 ^{Mw 32}	Constante Triángulo Calabi ³⁵		${C_{_{CR}}}$	${1 \over 3} + {(-23 + 3i \sqrt{237})^{\tfrac13} \over 3 \cdot 2^{\tfrac23}} + {11 \over 3 (2 (-23 + 3i \sqrt{237}))^{\tfrac13}}$	FindRoot[ 2x^3-2x^2-3x+2 ==0, {x, 1.5}, WorkingPrecision->40]	A	A046095	[1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...]	1946 ~	1.55138752454832039226195251026462381
0,97027 01143 92033 92574 ^{Mw 33}	Constante de Lochs ³⁶		${\text{£}_{_{Lo}}}$	$\frac {6 \ln 2 \ln 10}{ \pi^2}$	6ln(2)ln(10)/Pi^2		A086819	[0;1,32,1,1,1,2,1,46,7,2,7,10,8,1,71,1,37,1,1,...]	1964	0.97027011439203392574025601921001083
1,30568 67 ≈ ^{Mw 34}	Dimensión fractal del círculo de Apolonio ³⁷		$\varepsilon$				A052483	[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]		1.3056867 ≈
0,00131 76411 54853 17810 ^{Mw 35}	Constante de Heath-Brown–Moroz³⁸		${C_{_{HBM}}}$	$\underset{p_n: \, {primo}}{\prod_{n = 1}^\infty \left(1-\frac{1}{p_n}\right)^7\left(1+\frac{7p_n+1}{p_n^2}\right)}$	N[prod[n=1 to ∞] {((1-1/prime(n))^7) (1+(7prime(n)+1) /(prime(n)^2))}]	T ?	A118228	[0;758,1,13,1,2,3,56,8,1,1,1,1,1,143,1,1,1,2,...]		0.00131764115485317810981735232251358
0,14758 36176 50433 27417 ^{Mw 36}	Constante gamma de Plouffe ³⁹		${{C}}$	$\frac{1}{\pi} \arctan {\frac{1}{2}} = \frac{1}{\pi}\sum_{n=0}^\infty \frac {(-1)^n}{(2^{2n+1})(2n+1)}$ $= \frac{1}{\pi} \left( \frac {1}{2} - \frac {1}{3 \cdot 2^3} +\frac {1}{5 \cdot 2^5} -\frac {1}{7 \cdot 2^7} +\cdots \right)$	Arctan(1/2)/Pi	T	A086203	[0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...]		0.14758361765043327417540107622474052
0,70523 01717 91800 96514 ^{Mw 37}	Constante Primorial Suma de productos de inverso de primos ⁴⁰		${P_\#}$	$\underset{ p_n: \, {primo}}{\sum_{n = 1}^\infty \frac{1}{p_n\#} = \frac{1}{2} + \frac{1}{6} + \frac{1}{30} + \frac{1}{210} + ... = \sum_{k = 1}^\infty \prod_{n = 1}^k \frac {1}{p_n}}$	Sum[k=1 to ∞](prod[n=1 to k]{1/prime(n)})	I	A064648	[0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...]		0.70523017179180096514743168288824851
0,29156 09040 30818 78013 ^{Mw 38}	Constante dimer 2D, recubrimiento con dominós ⁴¹ · ⁴²		${\frac{C}{\pi}}$ C=catalan	$\int\limits_{-\pi}^{\pi} \frac{\cosh^{-1}\left(\frac{\sqrt{\cos(t)+3}}{\sqrt2}\right)}{4\pi}dt$	N[int[-pi to pi] {arccosh(sqrt( cos(t)+3)/sqrt(2)) /(4*Pi) /, dt}]		A143233	[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]		0.29156090403081878013838445646839491
0,72364 84022 98200 00940 ^{Mw 39}	Constante de Sarnak		${C_{sa} }$	$\prod_{p>2} \Big(1 - \frac{p+2}{p^3}\Big)$	N[prod[k=2 to ∞] {1-(prime(k)+2) /(prime(k)^3)}]	T ?	A065476	[0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...]		0.72364840229820000940884914980912759
0,63212 05588 28557 67840 ^{Mw 40}	Constante de tiempo⁴³		${\tau}$	$\lim_{n \to \infty} 1-\frac {!n}{n!}=\lim_{n \to \infty} P(n)= \int_{0}^{1}e^{-x}dx = 1-\frac{1}{e} =$ $\sum \limits_{n=0}^{\infty} \frac{(-1)^{n}}{n!} = \frac{1}{1!}-\frac{1}{2!}+\frac{1}{3!}-\frac{1}{4!}+\frac{1}{5!}-\frac{1}{6!}+\cdots$	lim_(n->∞) (1- !n/n!) !n=subfactorial	T	A068996	[0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [0;1,1,1,2n], n∈ℕ		0.63212055882855767840447622983853913
0.30366 30028 98732 65859 ^{Mw 41}	Constante de Gauss-Kuzmin-Wirsing⁴⁴		${\lambda}_{2}$	$\lim_{n \to \infty}\frac{F_n(x) - \ln(1 - x)}{(-\lambda)^n} = \Psi(x),$ donde $\Psi(x)$ es una función analítica tal que $\Psi(0) \!=\! \Psi(1) \!=\! 0$ .			A038517	[0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...]	1973	0.30366300289873265859744812190155623
1,30357 72690 34296 39125 ^{Mw 42}	Constante de Conway⁴⁵		${\lambda}$	$\begin{smallmatrix} x^{71}\quad\ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\ -x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\ +x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\ -12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\ -10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad\ -7x^{21}+9x^{20}\\ +3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\ +5x^{9}+x^{7}\quad\ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0 \quad\quad\quad \end{smallmatrix}$		A	A014715	[1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...]	1987	1.30357726903429639125709911215255189
1,18656 91104 15625 45282 ^{Mw 43}	Constante de Khinchin-Lévy ⁴⁶		${\beta}$	$\frac {\pi^2}{12\,\ln 2}$	pi^2 /(12 ln 2)		A100199	[1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...]	1935	1.18656911041562545282172297594723712
0,83564 88482 64721 05333	Constante de Baker ⁴⁷		$\beta_3$	$\int^1_0 \frac{{\mathrm{d} t}}{1 + t^3}=\sum_{n = 0}^\infty \frac{(-1)^n}{3n+1}= \frac{1}{3}\left(\ln 2+\frac{\pi}{\sqrt{3}}\right)$	Sum[n=0 to ∞] {((-1)^(n))/(3n+1)}		A113476	[0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...]		0.83564884826472105333710345970011076
23,10344 79094 20541 6160 ^{Mw 44}	Serie de Kempner(0)⁴⁸		${K_0}$	$1{+}\frac12{+}\frac13{+}\cdots{+}\frac19{+}\frac1{11}{+}\cdots{+}\frac1{19}{+}\frac1{21}{+}\cdots{+}\,\text{etc.}$ ${+}\frac1{99}{+}\frac1{111}{+}\cdots{+}\frac1{119}{+}\frac1{121}{+}\cdots\;\; \overset {Excluidos \; los} \underset{ contienen \; ceros.} {\scriptstyle denominadores \; que}$	1+1/2+1/3+1/4+1/5 +1/6+1/7+1/8+1/9 +1/11+1/12+1/13 +1/14+1/15+...		A082839	[23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...]		23.1034479094205416160340540433255981
0,98943 12738 31146 95174 ^{Mw 45}	Constante de Lebesgue ⁴⁹		${C_1}$	$\lim_{n\to\infty}\!\! \left(\!{L_n{-}\frac{4}{\pi^2}\ln(2n{+}1)}\!\!\right)\!{=} \frac{4}{\pi^2}\!\left({\sum_{k=1}^\infty \!\frac{2\ln k}{4k^2{-}1}} {-}\frac{\Gamma'(\tfrac12)}{\Gamma(\tfrac12)}\!\!\right)$	4/pi^2[(2 Sum[k=1 to ∞] {ln(k)/(4k^2-1)}) -poligamma(1/2)]		A243277	[0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...]		0.98943127383114695174164880901886671
1,38135 64445 18497 79337	Constante Beta Kneser-Mahler ⁵⁰		$\beta$	$e^{^{\textstyle{\frac{2}{\pi}} \displaystyle{\int_0^{\frac{\pi}{3}}} \textstyle{t \tan t\ dt}}} = e^{^{\displaystyle{\,\int_{\frac{-1}{3}}^{\frac{1}{3}}} \textstyle{\,\ln \lfloor 1+e^{2 \pi i t}} \rfloor dt}}$	e^((PolyGamma(1,4/3) - PolyGamma(1,2/3) +9)/(4sqrt(3)Pi))		A242710	[1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...]	1963	1.38135644451849779337146695685062412
1,18745 23511 26501 05459 ^{Mw 46}	Constante de Foias _α⁵¹		$F_\alpha$	$x_{n+1} = \left( 1 + \frac{1}{x_n} \right)^n\text{ para }n=1,2,3,\ldots$ La constante de Foias es el único número real tal que si x₁ = α, entonces la secuencia diverge a ∞. Cuando x₁ = α, $\, \lim_{n\to\infty} x_n \tfrac{\log n}{n} = 1$			A085848	[1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...]	1970	1.18745235112650105459548015839651935
2,29316 62874 11861 03150 ^{Mw 47}	Constante de Foias _β		$F_\beta$	$x^{x+1} = (x+1)^x$	x^(x+1) = (x+1)^x		A085846	[2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...]	2000	2.29316628741186103150802829125080586
0,66170 71822 67176 23515 ^{Mw 48}	Constante de Robbins⁵²		$\Delta(3)$	$\frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5}$	(4+172^(1/2)-6 3^(1/2)+21ln(1+ 2^(1/2))+42ln(2+ 3^(1/2))-7*Pi)/105		A073012	[0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...]	1978	0.66170718226717623515583113324841358
0,78853 05659 11508 96106 ^{Mw 49}	Constante de Lüroth⁵³		$C_L$	$\sum_{n = 2}^\infty \frac{\ln\left(\frac{n}{n-1}\right)}{n}$	Sum[n=2 to ∞] log(n/(n-1))/n		A085361	[0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...]		0.78853056591150896106027632216944432
0,92883 58271 ^{Mw 50}	Constante entre primos gemelos de JJGJJG ⁵⁴		$B_1$	$\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+\frac{1}{18}+\frac{1}{30}+\frac{1}{42}+\frac{1}{60}+\frac{1}{72}+\cdots$	1/4 + 1/6 + 1/12 + 1/18 + 1/30 + 1/42 + 1/60 + 1/72 + ...		A241560	[0; 1, 13, 19, 4, 2, 3, 1, 1]	2014	0.928835827131
5,24411 51085 84239 62092 ^{Mw 51}	Constante 2 Lemniscata ⁵⁵		$2\varpi$	$\frac{[\Gamma(\tfrac14)]^2}{\sqrt{2 \pi}} = 4\int^1_0 \frac{dx}{\sqrt{(1-x^2)(2-x^2)}}$	Gamma[ 1/4 ]^2 /Sqrt[ 2 Pi ]		A064853	[5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...]	1718	5.24411510858423962092967917978223883
0,57595 99688 92945 43964 ^{Mw 52}	Constante Stephens⁵⁶		$C_S$	$\prod_{n = 1}^\infty \left(1 - \frac{p}{p^3-1}\right)$	Prod[n=1 to ∞] {1-prime(n) /(prime(n)^3-1)}	T ?	A065478	[0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...]	?	0.57595996889294543964316337549249669
0,73908 51332 15160 64165 ^{Mw 53}	Número de Dottie ⁵⁷		$d$	$\lim_{x\to \infty} \cos^x(c) = \underbrace{\cos(\cos(\cos(\cos(\cdots(\cos(c))))))}_x$	cos(c)=c	T	A003957	[0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...]		0.73908513321516064165531208767387340
0,67823 44919 17391 97803 ^{Mw 54}	Constante Taniguchi⁵⁸		$C_T$	$\prod_{n = 1}^\infty \left(1 - \frac{3}{{p_n}^3}+\frac{2}{{p_n}^4}+\frac{1}{{p_n}^5}-\frac{1}{{p_n}^6}\right)$ $\scriptstyle p_{n}= \, \text{primo}$	Prod[n=1 to ∞] {1 -3/prime(n)^3 +2/prime(n)^4 +1/prime(n)^5 -1/prime(n)^6}	T ?	A175639	[0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...]	?	0.67823449191739197803553827948289481
1,35845 62741 82988 43520 ^{Mw 55}	Constante espiral áureaWolfram Mathematica. Golden Spiral.

c

\varphi ^ \frac{2}{\pi} = \left(\frac{1 + \sqrt{5}}{2}\right)^{\frac{2}{\pi}}

GoldenRatio^(2/Pi)A212224[1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...]1.35845627418298843520618060050187945 2,79128 78474 77920 00329Raíces anidadas S₅

S_{5}

\displaystyle \frac{\sqrt{21}+1}{2} = \scriptstyle \, \sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5+\cdots}}}}}\;

= 1+ \, \scriptstyle \sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\cdots}}}}}\;

(sqrt(21)+1)/2AA222134[2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...]
[2;1,3]2.79128784747792000329402359686400424 1,85407 46773 01371 91843 ^{Mw 56}Constante Lemniscata de Gauss ⁵⁹

L \text{/}\sqrt{2}

\int\limits_0^\infty \frac{{\mathrm{d} x}}{\sqrt{1 + x^4}} = \frac {1}{4\sqrt{\pi}} \,\Gamma \left(\frac {1}{4}\right)^2 = \frac{4 \left(\frac {1}{4}!\right)^2} {\sqrt{\pi}}

Γ() = Función Gamma pi^(3/2)/(2 Gamma(3/4)^2)A093341[1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...]?1.85407467730137191843385034719526005 1,75874 36279 51184 82469Constante Producto infinito, con Alladi-Grinstead ⁶⁰

Pr_1

\prod_{n = 2}^\infty \Big(1 + \frac{1}{n}\Big)^\frac{1}{n}

Prod[n=2 to ∞]
{(1+1/n)^(1/n)}A242623[1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...]19771.75874362795118482469989684865589317 1,73245 47146 00633 47358 ^{Ow 4}Constante inversa de Euler-Mascheroni

\frac {1}{\gamma}

\left(\int_{0}^{1} -\log \left(\log \frac{1}{x}\right)\, dx\right)^{-1} = \sum_{n=1}^\infty (-1)^n (-1+\gamma)^n

1/Integrate_
(x=0 to 1)
{-log(log(1/x))}A098907[1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...]1.73245471460063347358302531586082968 1,94359 64368 20759 20505 ^{Mw 57}Constante
Euler Totient ⁶¹ ⁶²

ET

\underset {p \text{= Nros. primos}} {\prod_{p} \Big(1 + \frac{1}{p(p-1)}\Big)} = \frac {\zeta(2)\;\zeta(3)}{\zeta(6)}=\frac {315 \;\zeta(3)}{2\pi^4}

zeta(2)*zeta(3)
/zeta(6)A082695[1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...]17501.94359643682075920505707036257476343 1,49534 87812 21220 54191Raíz cuarta de cinco⁶³

\sqrt[4]{5}

\sqrt[5]{5 \,\sqrt[5]{5 \, \sqrt[5]{5 \,\sqrt[5]{5 \,\sqrt[5]{5 \,\cdots}}}}}

(5(5(5(5(5(5(5)
^1/5)^1/5)^1/5)
^1/5)^1/5)^1/5)
^1/5 ...AA011003[1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...]1.49534878122122054191189899414091339 0,87228 40410 65627 97617 ^{Mw 58}Área Círculo de Ford⁶⁴

A_{CF}

\sum_{q\ge 1} \sum_{ (p, q)=1 \atop 1 \le p < q }\pi \left( \frac{1}{2 q^2} \right)^2 = \frac{\pi}{4} \frac{\zeta(3)}{\zeta(4)} = \frac{45}{2} \frac{\zeta(3)}{\pi^3}

ς() = Función zeta pi Zeta(3) /(4 Zeta(4))[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...]?0.87228404106562797617519753217122587 1,08232 32337 11138 19151 ^{Mw 59}Constante Zeta(4) ⁶⁵

\zeta(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} + ...

Sum[n=1 to ∞]
{1/n^4}TA013662[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,...]1.08232323371113819151600369654116790 1,56155 28128 08830 27491Raíz Triangular de 2.⁶⁶

{R_2}

\frac{\sqrt{17}-1}{2} = \,\scriptstyle \sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\cdots}}}}}} \,\, -1

= \,\scriptstyle \sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\cdots}}}}}} \textstyle

(sqrt(17)-1)/2AA222133[1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...]
[1;1,1,3]1.56155281280883027491070492798703851 1,45607 49485 82689 67139 ^{Mw 60}Constante de Backhouse ⁶⁷

{B}

\lim_{k \to \infty}\left | \frac{q_{k+1}}{q_k} \right \vert \quad \scriptstyle \text {donde:} \displaystyle \;\; Q(x)=\frac{1}{P(x)}= \! \sum_{k=1}^\infty q_k x^k

P(x) = \! \sum_{k=1}^\infty \underset{p_k: \, {primo}}{p_k x^k} \!\! = 1{+}2x{+}3x^2{+}5x^3{+}7x^4{+}...

1/( FindRoot[0 == 1
+ Sum[x^n Prime[n],
{n, 10000}], {x, {1}})A072508[1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,4,...]19951.45607494858268967139959535111654355 1,43599 11241 76917 43235 ^{Mw 61}Constante interpolación de Lebesgue ⁶⁸ · ⁶⁹

{L_1}

\prod_{\begin{smallmatrix}i=0\\ j\neq i\end{smallmatrix}}^{n} \frac{x-x_i}{x_j-x_i} = \frac {1}{\pi} \int_0^{\pi} \frac {\lfloor \sin{\frac{3 t}{2}}\rfloor}{\sin{\frac{t}{2}}}\, dt = \frac {1}{3} + \frac {2 \sqrt{3}}{\pi}

1/3 + 2*sqrt(3)/PiTA226654[1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...]1902 ~1.43599112417691743235598632995927221 1,04633 50667 70503 18098Constante mass Minkowski-Siegel ⁷⁰

F_1

\prod_{n=1}^{\infty} \frac{n!}{\sqrt{2\pi n}\left(\frac{n}{e}\right)^n \sqrt[12]{1+\tfrac1{n}}}

N[prod[n=1 to ∞]
n! /(sqrt(2*Pi*n)
*(n/e)^n *(1+1/n)
^(1/12))]A213080[1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..]1867
1885
19351.04633506677050318098095065697776037 1,86002 50792 21190 30718Constante
espiral de
Theodorus ⁷¹

\partial

\sum_{n=1}^{\infty} \frac{1}{\sqrt{n^3} + \sqrt{n}} = \sum_{n=1}^{\infty} \frac{1}{\sqrt{n} (n+1)}

Sum[n=1 to ∞]
{1/(n^(3/2)
+n^(1/2))}A226317[1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...]-460
a
-3991.86002507922119030718069591571714332 0,80939 40205 40639 13071 ^{Mw 62}Constante de Alladi-Grinstead⁷²

{\mathcal{A}_{AG}}

e^{-1+\sum \limits_{k=2}^\infty \sum \limits_{n=1}^\infty \frac{1}{n k^{n+1}}} = e^{-1-\sum \limits_{k=2}^\infty \frac{1}{k} \ln \left( 1-\frac{1}{k}\right)}

e^{(sum[k=2 to ∞]
|sum[n=1 to ∞]
{1/(n k^(n+1))})-1}A085291[0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...]19770.80939402054063913071793188059409131 1,26185 95071 42914 87419 ^{Mw 63}Dimensión fractal delCopo de nieve de Koch ⁷³

{C_k}

\frac{\log 4}{\log 3}

log(4)/log(3)TA100831[1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...]1.26185950714291487419905422868552171 1,22674 20107 20353 24441 ^{Mw 64}Constante Factorial de Fibonacci ⁷⁴

F

\prod_{n = 1}^\infty \left(1 - \left( -\frac{1}{{\varphi}^2}\right)^n \right)= \prod_{n = 1}^\infty \left(1 - \left( \frac{\sqrt{5}-3}{2}\right)^n \right)

prod[n=1 to ∞]
{1-((sqrt(5) -3)/2)^n}A062073[1;4,2,2,3,2,15,9,1,2,1,2,15,7,6,21,3,5,1,23,...]1.22674201072035324441763023045536165 0,85073 61882 01867 26036 ^{Mw 65}Constante de plegado de papel ⁷⁵ ·⁷⁶

{P_f}

\sum_{n=0}^{\infty} \frac {8^{2^n}}{2^{2^{n+2}}-1} = \sum_{n=0}^{\infty} \cfrac {\tfrac {1}{2^{2^n}}} {1-\tfrac{1}{2^{2^{n+2}}}}

N[Sum[n=0 to ∞]
{8^2^n/(2^2^
(n+2)-1)},37]A143347[0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...]?0.85073618820186726036779776053206660 6,58088 59910 17920 97085Constante de Froda ⁷⁷

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,...]6.58088599101792097085154240388648649 – 0,5
± 0,86602 54037 84438 64676 iRaíz cúbica de 1 ⁷⁸

\sqrt[3]{1}

\begin{cases} \ \ 1 \\ -\frac{1}{2}+\frac{\sqrt{3}}{2}i \\ -\frac{1}{2}-\frac{\sqrt{3}}{2}i. \end{cases}

1,
E^(2i pi/3) ,
E^(-2i pi/3)C AA010527- [0,5]
± [0;1,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] i
- [0,5]
± [0; 1, 6, 2] i- 0,5
± 0.8660254037844386467637231707529 i 1,11786 41511 89944 97314 ^{Mw 66}Constante de Goh-Schmutz ⁷⁹

C_{GS}

\int^\infty_0\frac{\log(s+1)}{e^s-1} \ ds = \! - \! \sum_{n=1}^\infty \frac {e^n}{n} Ei(-n) \overset {Ei:} \underset{ Exponencial} {\scriptstyle Integral}

Integrate{
log(s+1)
/(E^s-1)}A143300[1;8,2,15,2,7,2,1,1,1,1,2,3,5,3,5,1,1,4,13,1,...]1.11786415118994497314040996202656544 1,11072 07345 39591 56175 ^{Mw 67}Razón entre un cuadrado y la circunferencia circunscrita ⁸⁰

\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)}TA093954[1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...]1.11072073453959156175397024751517342 2,82641 99970 67591 57554 ^{Mw 68}Constante de Murata⁸¹

{C_m}

\prod_{n = 1}^\infty \underset{p_{n}: \, {primo}}{ \Big(1 + \frac{1}{(p_n-1)^2}\Big)}

Prod[n=1 to ∞]
{1+1/(prime(n)
-1)^2}T ?A065485[2;1,4,1,3,5,2,2,2,4,3,2,1,3,2,1,1,1,8,2,2,28,...]2.82641999706759157554639174723695374 1,52362 70862 02492 10627 ^{Mw 69}Dimensión fractal de la frontera de la Curva del dragón ⁸²

{C_d}

{\frac{\log\left(\frac{1+\sqrt[3]{73-6\sqrt{87}}+\sqrt[3]{73+6\sqrt{87}}}{3}\right)} {\log(2)}}

(log((1+(73-6
sqrt(87))^1/3+ (73+6 sqrt(87))^1/3)
/3))/ log(2)))T[1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1,...]1.52362708620249210627768393595421662 1,30637 78838 63080 69046 ^{Mw 70}Constante de Mills ⁸³

{\theta}

Es primo

\lfloor \theta^{3^{n}} \rfloor

Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8)A051021[1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2,...]19471.30637788386308069046861449260260571 2,02988 32128 19307 25004 ^{Mw 71}Volumen hiperbólico del Complemento del Nudo en Forma de Ocho ⁸⁴

{V_{8}}

2 \sqrt{3}\, \sum_{n=1}^\infty \frac{1}{n {2n \choose n}} \sum_{k=n}^{2n-1} \frac{1}{k} = 6 \int \limits_{0}^{\pi / 3} \log \left( \frac{1}{2 \sin t} \right) \, dt =

\scriptstyle \frac{\sqrt{3}}{{9}}\, \sum \limits_{n=0}^\infty \frac{(-1)^n}{27^n}\,\left\{\! \frac{{18}}{(6n+1)^2} - \frac{{18}}{(6n+2)^2} - \frac{{24}}{(6n+3)^2} - \frac{{6}}{(6n+4)^2} + \frac{{2}}{(6n+5)^2}\!\right\}

6 integral[0 to pi/3]
{log(1/(2 sin (n)))}A091518[2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1,...]2.02988321281930725004240510854904057 1,46707 80794 33975 47289 ^{Mw 72}Constante de Porter⁸⁵

{C}

\frac{6\ln 2}{\pi ^2} \left(3 \ln 2 + 4 \,\gamma -\frac{24}{\pi ^2} \,\zeta '(2)-2 \right)-\frac{1}{2}

\scriptstyle \gamma \, \text{= Constante de Euler–Mascheroni = 0,5772156649...}

\scriptstyle \zeta '(2) \,\text{= Derivada de }\zeta(2) \,= \, - \!\!\sum \limits_{n = 2}^{\infty} \frac{\ln n}{n^2} \,\text{= −0,9375482543...}

6*ln2/Pi^2(3*ln2+ 4 EulerGamma- WeierstrassZeta'(2) *24/Pi^2-2)-1/2A086237[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...]19741.46707807943397547289779848470722995 1,85193 70519 82466 17036 ^{Mw 73}Constante de Gibbs ⁸⁶

{Si(\pi)}

Integral
senoidal

\int_0^{\pi} \frac {\sin t}{t}\, dt = \sum \limits_{n=1}^\infty (-1)^{n-1} \frac{\pi^{2n-1}}{(2n-1)(2n-1)!}

= \pi- \frac{\pi^3}{3*3!} + \frac{\pi^5}{5*5!} - \frac{\pi^7}{7*7!} + ...

SinIntegral[Pi]A036792[1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,...]1.85193705198246617036105337015799136 1,78221 39781 91369 11177 ^{Mw 74}Constante de Grothendieck ⁸⁷

{K_{R}}

\frac {\pi}{2 \log(1+\sqrt{2})} = \frac {\pi}{2 \operatorname{arsinh} 1}

pi/(2 log(1+sqrt(2)))A088367[1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3,...]1.78221397819136911177441345297254934 1,74540 56624 07346 86349 ^{Mw 75}Constante media armónica de Khinchin⁸⁸

{K_{-1}}

\frac {\log 2} {\sum \limits_{n=1}^\infty \frac {1}{n} \log\bigl(1+\frac{1}{n(n+2)}\bigr)} = \lim_{n \to \infty} \frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}}

a₁...a_n son elementos de una fracción continua [a₀;a₁,a₂,...,a_n]

(log 2)/
(sum[n=1 to ∞]
{1/n log(1+
1/(n(n+2))}A087491[1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1,...]1.74540566240734686349459630968366106 0,10841 01512 23111 36151 ^{Mw 76}Constante de Trott

⁸⁹

\mathrm{T}_1

\textstyle [1, 0, 8, 4, 1, 0, 1, 5, 1, 2, 2, 3, 1, 1, 1, 3, 6,...]

\frac 1{1+\frac 1{0+\frac 1{8+\frac 1{4+\frac 1{1+\frac 1{0+1{/...}}}}}}}

Trott ConstantA039662[0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2,...]0.10841015122311136151129081140641509 1,45136 92348 83381 05028 ^{Mw 77}Constante de Ramanujan–Soldner⁹⁰ · ⁹¹

{\mu}

\mathrm{Li}(x) = \int_0^x \frac{dt}{\ln t} = 0 \qquad \mathrm{Li} \, \scriptstyle \text{= Integral logarítmica}

\mathrm{Li}(x)\;=\;\mathrm{Ei}(\ln{x}) \; \; \qquad \mathrm{Ei} \, \scriptstyle \text{= Integral exponencial}

FindRoot[li(x) = 0]IA070769[1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1,...]1792
a
18091.45136923488338105028396848589202744 0,64341 05462 88338 02618 ^{Mw 78}Constante de Cahen⁹²

\xi _{2}

\sum_{k=1}^{\infty} \frac{(-1)^{k}}{s_k-1} = \frac{1}{1} - \frac{1}{2} + \frac{1}{6} - \frac{1}{42} + \frac{1}{1806} {\,\pm \cdots}

s_k son términos de la Sucesión de Sylvester 2, 3, 7, 43, 1807 ...
Definida por

\scriptstyle \, S_{0}= \, 2 , \,\, S_{k}= \, 1+\prod \limits_{n=0}^{k-1} S_{n}

para k>0

TA118227[0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...]18910.64341054628833802618225430775756476 -4,22745 35333 76265 408 ^{Mw 79}Digamma (¼) ⁹³

\psi (\tfrac14)

-\gamma -\frac{\pi}{2} - 3\ln{2} = -\gamma+\sum_{n=0}^{\infty}\left(\frac{1}{n+1}-\frac{1}{n+\tfrac14}\right)

-EulerGamma
-\pi/2 -3 log 2A020777-[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4,...]-4,2274535333762654080895301460966835 1,77245 38509 05516 02729 ^{Mw 80}Constante de Carlson-Levin⁹⁴

{\Gamma}(\tfrac12)

\sqrt{\pi} = \left(-\frac{1}{2}\right)! = \int_{-\infty }^{\infty } \frac {1}{e^{x^2}} \, dx = \int_{0 }^{1} \frac {1}{\sqrt{-\ln x}} \, dx

sqrt (pi)TA002161[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]1.77245385090551602729816748334114518 0,23571 11317 19232 93137 ^{Mw 81}Constante de Copeland-Erdős⁹⁵

{\mathcal{C}_{CE}}

\sum _{n=1}^\infty \frac{p_n} {10^{n + \sum \limits_{k=1}^n \lfloor \log_{10}{p_k} \rfloor }}

sum[n=1 to ∞]
{prime(n) /(n+(10^
sum[k=1 to n]{floor
(log_10 prime(k))}))}IA033308[0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,...]0.23571113171923293137414347535961677 2,09455 14815 42326 59148 ^{Mw 82}Constante de Wallis⁹⁶

W

\sqrt[3]{\frac{45-\sqrt{1929}}{18}}+\sqrt[3]{\frac{45+\sqrt{1929}}{18}}

(((45-sqrt(1929))
/18))^(1/3)+
(((45+sqrt(1929))
/18))^(1/3)AA007493[2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...]1616
a
17032.09455148154232659148238654057930296 0,28674 74284 34478 73410 ^{Mw 83}Constante Strongly Carefree⁹⁷

K_{2}

\prod_{n=1}^\infty \underset{p_{n}: \, {primo}} {\left( 1-\frac{3 p_n-2}{{p_n}^{3}}\right)} = \frac {6}{\pi ^2}\prod_{n=1}^\infty \underset{p_{n}: \, {primo}} {\left( 1-\frac{1}{{p_n(p_n+1)}}\right)}

N[ prod[k=1 to ∞]
{1 - (3*prime(k)-2)
/(prime(k)^3)}]A065473[0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7,...]0.28674742843447873410789271278983845 0,64624 54398 94813 30426 ^{Mw 84}Constante de Masser-Gramain ⁹⁸

{C}

\gamma {\beta}(1){+}{\beta}'(1) = \pi \! \left(-\!\ln \Gamma(\tfrac14)+\tfrac34 \pi+\tfrac12 \ln 2+\tfrac12 \gamma \right)

= \pi \! \left(-\!\ln (\tfrac14 !)+\tfrac34 \ln \pi -\tfrac32 \ln 2+\tfrac12 \, \gamma \right)

\scriptstyle \gamma \, \text{= Constante de Euler–Mascheroni = 0,5772156649...}

β() = Función beta, Γ() = Función Gamma Pi/4*(2*Gamma
+ 2*Log[2]
+ 3*Log[Pi]
- 4 Log[Gamma[1/4]])A086057[0;1,1,1,4,1,3,2,3,9,1,33,1,4,3,3,5,3,1,3,4,...]0.64624543989481330426647339684579279 0,54325 89653 42976 70695 ^{Mw 85}Constante de Bloch-Landau ⁹⁹

{L}

\frac {\Gamma(\tfrac13)\;\Gamma(\tfrac{5}{6})} {\Gamma(\tfrac{1}{6})} = \frac {(-\tfrac23)!\;(-1+\tfrac56)!} {(-1+\tfrac16)!}

gamma(1/3)
*gamma(5/6)
/gamma(1/6)A081760[0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...]19290.54325896534297670695272829530061323 0,34053 73295 50999 14282 ^{Mw 86}Constante de Pólya Random Walk¹⁰⁰

{p(3)}

1- \!\!\left({3\over(2\pi)^3}\int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} {dx\,dy\,dz\over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}

= 1- 16\sqrt{\tfrac23}\;\pi^3 \left(\Gamma(\tfrac{1}{24})\Gamma(\tfrac{5}{24})\Gamma(\tfrac{7}{24})\Gamma(\tfrac{11}{24})\right)^{-1}

1-16*Sqrt[2/3]*Pi^3
/((Gamma[1/24]
*Gamma[5/24]
*Gamma[7/24]
*Gamma[11/24])A086230[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...]0.34053732955099914282627318443290289 0,35323 63718 54995 98454 ^{Mw 87}Constante de Hafner-Sarnak-McCurley (1)¹⁰¹

{\sigma}

\prod_{k=1}^{\infty}\left\{1-\left[1-\prod_{j=1}^n(1-p_k^{-j})\right]^2\right\}

prod[k=1 to ∞] {1-(1-prod[j=1 to n] {1-prime(k)^-j})^2}A085849[0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...]19930.35323637185499598454351655043268201 0,74759 79202 53411 43517 ^{Mw 88}Constante Parking de Rényi¹⁰²

{m}

\int \limits_{0}^{\infty} e^{\left(\! -2 \int \limits_{0}^{x} \frac {1-e^{-y}}{y} dy\right)}\! dx = {e^{-2 \gamma}} \int \limits_{0}^{\infty} \frac{e^{-2 \Gamma(0,n)}}{n^2}

[e^(-2*Gamma)] * Int{n,0,∞}[ e^(- 2*Gamma(0,n)) /n^2]A050996[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...]19580.74759792025341143517873094383017817 0,60792 71018 54026 62866 ^{Mw 89}Constante de Hafner-Sarnak-McCurley (2)¹⁰³

\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/prime(n)^2)TA059956[0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...]0.60792710185402662866327677925836583 0,12345 67891 01112 13141 ^{Mw 90}Constante de Champernowne¹⁰⁴

C_{10}

\sum_{n=1}^\infty\sum_{k=10^{n-1}}^{10^n-1}\frac{k}{10^{kn-9\sum_{j=0}^{n-1}10^j(n-j-1)}}

TA033307[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...]19330.12345678910111213141516171819202123 0,76422 36535 89220 66299 ^{Mw 91}Constante de Landau-Ramanujan¹⁰⁵

K

\frac1{\sqrt2}\prod_{p\equiv3\!\!\!\!\!\mod \! 4}\!\! \underset{\!\!\!\!\!\!\!\! p: \, {primo}}{\left(1-\frac1{p^2}\right)^{-\frac{1}{2}}}\!\!=\frac\pi4\prod_{p\equiv1\!\!\!\!\!\mod \!4}\!\! \underset{\!\!\!\! p: \, {primo}}{\left(1-\frac1{p^2}\right)^\frac{1}{2}}

T ?A064533[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...]19080.76422365358922066299069873125009232 1,58496 25007 21156 18145 ^{Mw 92}Dimensión Hausdorfdel triángulo de Sierpinski¹⁰⁶

{log_2 3}

\frac {log 3}{log 2} = \frac{\sum_{n=0}^\infty \frac{1}{2^{2n+1}(2n+1)}}{\sum_{n=0}^\infty \frac{1}{3^{2n+1}(2n+1)}} = \frac{\frac{1}{2}+\frac{1}{24}+\frac{1}{160}+...}{\frac{1}{3}+\frac{1}{81}+\frac{1}{1215}+...}

( Sum[n=0 to ∞]
{1/(2^(2n+1)(2n+1))})/
( Sum[n=0 to ∞]
{1/(3^(2n+1)(2n+1))})TA020857[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]1.58496250072115618145373894394781651 0,11000 10000 00000 00000 0001 ^{Mw 93}Número de Liouville¹⁰⁷

\text{£}_{Li}

\sum_{n=1}^\infty \frac{1}{10^{n!}} = \frac {1}{10^{1!}} + \frac{1}{10^{2!}} + \frac{1}{10^{3!}} + \frac{1}{10^{4!}} + ...

Sum[n=1 to ∞]
{10^(-n!)}TA012245[1;9,1,999,10,9999999999999,1,9,999,1,9]0.11000100000000000000000100... 0,46364 76090 00806 11621Serie de Machin-Gregory¹⁰⁸

\arctan \frac {1}{2}

\underset{Para \; x = 1/2 \qquad \qquad} {\sum_{n=0}^\infty \frac{\!\!(-1)^n x^{2n+1}}{2n+1} = \frac {1}{2} - \! \frac{1}{3 \cdot 2^3} {+} \frac{1}{5 \cdot 2^5} - \! \frac{1}{7 \cdot 2^7} {+}{...}}

Sum[n=0 to ∞]
{(-1)^n (1/2)
^(2n+1)/(2n+1)}IA073000[0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...]0.46364760900080611621425623146121440 1,27323 95447 35162 68615Serie de Ramanujan-Forsyth ¹⁰⁹

\frac {4}{\pi}

\displaystyle \sum \limits_{n=0}^{\infty} \textstyle \left(\frac{(2n-3)!!}{(2n)!!}\right)^{2} = {1 \! + \! \left(\frac {1}{2} \right)^2 \! {+} \left(\frac {1}{2 \cdot 4} \right)^2 \! {+} \left(\frac {1 \cdot 3}{2 \cdot 4 \cdot 6} \right)^2 {+} ...}

Sum[n=0 to ∞]
{[(2n-3)!!
/(2n)!!]^2}IA088538[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]1.27323954473516268615107010698011489 15,15426 22414 79264 1897 ^{Mw 94}Constante exponencial reiterado¹¹⁰

e^e

\sum_{n=0}^\infty \frac{e^n}{n!} = \lim_{n \to \infty} \left(\frac {1+n}{n} \right)^{n^{-n}(1+n)^{1+n}}

Sum[n=0 to ∞]
{(e^n)/n!}A073226[15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,...]15.1542622414792641897604302726299119 36,46215 96072 07911 77099Pi elevado a pi ¹¹¹

\pi ^\pi

\pi ^\pi

pi^piA073233[36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2,...]36.4621596072079117709908260226921236 0,53964 54911 90413 18711Constante de Ioachimescu ¹¹²

2+\zeta(\tfrac12)

{2{-}(1{+}\sqrt{2})\sum_{n=1}^\infty \frac{(-1)^{n+1}}{\sqrt{n}}} = \gamma + \sum_{n=1}^\infty \frac{(-1)^{2n} \; \gamma_n}{2^n n!}

γ +N
[sum[n=1 to ∞]
{((-1)^(2n)
gamma_n)
/(2^n n!)}]2-
A059750[0;1,1,5,1,4,6,1,1,2,6,1,1,2,1,1,1,37,3,2,1,...]0.53964549119041318711050084748470198 2,58498 17595 79253 21706 ^{Mw 95}Constante de Sierpiński ¹¹³

{K}

\pi\left(2\gamma+\ln\frac{4\pi^3}{\Gamma(\tfrac{1}{4})^4}\right) = \pi (2 \gamma + 4 \ln\Gamma(\tfrac{3}{4}) - \ln\pi)

= \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma (\tfrac{1}{4})\right)

-Pi Log[Pi]+2 Pi
EulerGamma
+4 Pi Log
[Gamma[3/4]]A062089[2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...]19072.58498175957925321706589358738317116 1,83928 67552 14161 13255Constante Tribonacci¹¹⁴

{\phi_{}}_3

\textstyle \frac{1+\sqrt[3]{19+3\sqrt{33}}+\sqrt[3]{19-3\sqrt{33}}}{3} = \scriptstyle \, 1+ \left(\sqrt[3]{\tfrac12 + \sqrt[3]{\tfrac12 + \sqrt[3]{\tfrac12 + ...}}}\right)^{-1}

(1/3)*(1+(19+3
*sqrt(33))^(1/3)
+(19-3
*sqrt(33))^(1/3))AA058265[1;1,5,4,2,305,1,8,2,1,4,6,14,3,1,13,5,1,7,...]1.83928675521416113255185256465328660 0,69220 06275 55346 35386 ^{Mw 96}Valor mínimo de la función
ƒ(x) = x^x ¹¹⁵

{\left(\frac{1}{e}\right)}^\frac{1}{e}

{e}^{-\frac{1}{e}}

= Inverso de: Número de Steiner e^(-1/e)A072364[0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]0.69220062755534635386542199718278976 0,70710 67811 86547 52440

+0,70710 67811 86547 52440 i

Raíz cuadrada de i ¹¹⁶

\sqrt{i}

\sqrt[4]{-1} = \frac{1+i}{\sqrt{2}} = e^ \frac{i\pi}{4} = \cos\left (\frac{\pi}{4} \right ) + i\sin\left ( \frac{\pi}{4} \right )

(1+i)/(sqrt 2)C AA010503

A010503[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..]
= [0;1,2,...]
[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] i
= [0;1,2,...] i0.70710678118654752440084436210484903
+ 0.70710678118654752440084436210484 i 1,15636 26843 32269 71685 ^{Mw 97}Constante de recurrencia cúbica ¹¹⁷

{\sigma_3}

\prod_{n=1}^\infty n^{{3}^{-n}} = \sqrt[3] {1 \sqrt[3] {2 \sqrt[3]{3 \cdots}}} = 1^{1/3} \; 2^{1/9} \; 3^{1/27} \cdots

prod[n=1 to ∞]
{n ^(1/3)^n}A123852[1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...]1.15636268433226971685337032288736935 1,66168 79496 33594 12129 ^{Mw 98}Recurrencia cuadrática de Somos¹¹⁸

{\sigma}

\prod_{n=1}^\infty n^{{1/2}^n} = \sqrt {1 \sqrt {2 \sqrt{3 \sqrt{4 \cdots}}}} = 1^{1/2} \; 2^{1/4} \; 3^{1/8} \cdots

prod[n=1 to ∞]
{n ^(1/2)^n}T ?A065481[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]1.66168794963359412129581892274995074 0,95531 66181 24509 27816Ángulo mágico¹¹⁹

{\theta_m}

\arctan \left(\sqrt{2}\right) = \arccos \left(\sqrt{\tfrac13}\right) \approx \textstyle {54,7356} ^{ \circ }

arctan(sqrt(2))TA195696[0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...]0.95531661812450927816385710251575775 0,59634 73623 23194 07434 ^{Mw 99}Constante de Euler-Gompertz ¹²⁰

{G}

-e \mathrm{Ei}(-1) = \int \limits_{0}^{\infty} \frac{e^{-n}}{1{+}n} \, dn = \textstyle {\frac 1 {1+\frac 1{1+\frac 1{1+\frac 2{1+\frac 2{1+\frac 3{1+\frac 3{1+4{/...}} }}}}}}}

N[int[0 to ∞]
{(e^-n)/(1+n)}]IA073003[0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...]0.59634736232319407434107849936927937 0,69777 46579 64007 98200 ^{Mw 100}Constante de fracción continua, función de Bessel ¹²¹

{C}_{CF}

\frac{I_1(2)}{I_0(2)} = \frac{ \sum \limits_{n = 0}^{\infty} \frac{n}{n!n!}} {{ \sum \limits_{n = 0}^{\infty} \frac{1}{n!n!}}} = \textstyle \frac 1{1+\frac 1{2+\frac 1{3+\frac 1{4+\frac 1{5+\frac 1{6+1{/...}}}}}}}

(Sum {n=0 to ∞}
n/(n!n!)) /
(Sum {n=0 to ∞}
1/(n!n!))IA052119[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...]
= [0;p+1], p∈ℕ0.69777465796400798200679059255175260 0,36651 29205 81664 32701Mediana distribución de Gumbel ¹²²

{ll_2}

-\ln(\ln(2))

-ln(ln(2))A074785[0;2,1,2,1,2,6,1,6,6,2,2,2,1,12,1,8,1,1,3,1,...]0.36816512920566432701243915823266947 0,56714 32904 09783 87299 ^{Mw 101}Constante Omega, función W(1) de Lambert ¹²³

{\Omega}

\sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!} =\,\left(\frac{1}{e}\right) ^{\left(\frac{1}{e}\right) ^{\cdot^{\cdot^{\left(\frac{1}{e}\right)}}}} = e^{-\Omega} = {e}^{-e^{-e^{\cdot^{\cdot^{{-e}}}}}}

Sum[n=1 to ∞]
{(-n)^(n-1)/n!}TA030178[0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...]1728
a
17770.56714329040978387299996866221035555 0.69034 71261 14964 31946Límite superior exponencial iterado¹²⁴

{H}_{2n+1}

\lim_{n \to \infty} {H}_{2n+1} = \textstyle \left(\frac{1}{2}\right) ^{\left(\frac{1}{3}\right) ^{\left(\frac{1}{4}\right) ^{\cdot^{\cdot^{\left(\frac{1}{2n+1}\right)}}}}} = {2}^{-3^{-4^{\cdot^{\cdot^{{-2n-1}}}}}}

2^-3^-4^-5^-6^
-7^-8^-9^-10^
-11^-12^-13 …A242760[0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,3,1,1,10,1,3,2,...]0.69034712611496431946732843846418942 0,65836 55992Límite inferior exponencial iterado¹²⁵

{H}_{2n}

\lim_{n \to \infty} {H}_{2n} = \textstyle \left(\frac{1}{2}\right) ^{\left(\frac{1}{3}\right) ^{\left(\frac{1}{4}\right) ^{\cdot^{\cdot^{\left(\frac{1}{2n}\right)}}}}} = {2}^{-3^{-4^{\cdot^{\cdot^{{-2n}}}}}}

2^-3^-4^-5^-6^
-7^-8^-9^-10^
-11^-12 …[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...]0.6583655992... 2,71828 18284 59045 23536 ^{Mw 102}Número e, constante de Euler ¹²⁶

{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

2\!\prod_{n=1}^{\infty}\!\!\textstyle\sqrt[2^n]{\frac{\prod_{i=1}^{2^{n-1}}(2^n+2i)}{\prod_{i=1}^{2^{n-1}}\!(2^n+2i-1)}} =2\sqrt{\frac{4}{3}}\sqrt[4]{\frac{6\cdot 8}{5\cdot 7}}\sqrt[8]{\frac{10\cdot 12\cdot 14\cdot 16}{9\cdot 11\cdot 13\cdot 15}}\cdots

Sum[n=0 to ∞]
{1/n!}TA001113[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...]
= [2;1,2p,1], p∈ℕ16182.71828182845904523536028747135266250 2,74723 82749 32304 33305Raíces anidadas de Ramanujan R₅ ¹²⁷

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)))/2A[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]2.74723827493230433305746518613420282 2,23606 79774 99789 69640^{Mw 103}Raíz cuadrada de cinco
Suma de Gauss ¹²⁸

\sqrt{5}

\scriptstyle (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)}AA002163[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...]
= [2;4,...]2.23606797749978969640917366873127624 1,09864 19643 94156 48573 ^{Mw 104}Constante París

C_{Pa}

\prod_{n=2}^\infty \frac{2 \varphi}{\varphi+ \varphi_n} \; ,\; \varphi {=} {Fi}

con

\varphi_n {=} \sqrt{1 {+} \varphi_{n {-} 1}}

\varphi_1 {=} 1

A105415[1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...]1.09864196439415648573466891734359621 0,11494 20448 53296 20070 ^{Mw 105}Constante de Kepler–Bouwkamp ¹²⁹

{\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)}

A085365[0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...]0.11494204485329620070104015746959874 1,28242 71291 00622 63687 ^{Mw 106}Constante de Glaisher–Kinkelin ¹³⁰

{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,...]18781.28242712910062263687534256886979172 3,62560 99082 21908 31193 ^{Mw 107}Gamma(1/4) ¹³¹

\Gamma(\tfrac14)

4 \left(\frac{1}{4}\right)! = (2 \pi)^{\frac{3}{4}} \prod_{k=1}^\infty \tanh \left( \frac{\pi k}{2} \right)

4(1/4)!TA068466[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]17293.62560990822190831193068515586767200 1,78107 24179 90197 98523 ^{Mw 108}Exp.gamma por función
G-Barnes ¹³²

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}A073004[1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...]19001,78107241799019798523650410310717954 0,18785 96424 62067 12024 ^{Mw 109}MRB Constant, Marvin Ray Burns ¹³³ ¹³⁴ ¹³⁵

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)}A037077[0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...]19990.18785964246206712024851793405427323 1,01494 16064 09653 62502 ^{Mw 110}Constante de Gieseking ¹³⁶

{\pi \ln \beta}

\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} {\pm} ... \right) = \displaystyle \!\int_0^{\frac{2\pi}{3}} \! \ln \!\left(2 \cos \tfrac t2 \right) {\mathrm d}t

sqrt(3)*3/4 *(1
-Sum[n=0 to ∞]
{1/((3n+2)^2)}
+Sum[n=1 to ∞]
{1/((3n+1)^2)})A143298[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]19121.01494160640965362502120255427452028 2,62205 75542 92119 81046 ^{Mw 111}Constante Lemniscata¹³⁷

{\varpi}

\pi \, {G} = 4 \sqrt{\tfrac2\pi}\,\Gamma{\left(\tfrac54 \right)^2} = \tfrac14 \sqrt{\tfrac{2}{\pi}}\,\Gamma {\left(\tfrac14 \right)^2} = 4 \sqrt{\tfrac2\pi}\left(\tfrac14 !\right)^2

4 sqrt(2/pi)
((1/4)!)^2TA062539[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]17982.62205755429211981046483958989111941 0,83462 68416 74073 18628 ^{Mw 112}Constante de Gauss¹³⁸

{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)TA014549[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]17990.83462684167407318628142973279904680 0,00787 49969 97812 3844 ^{Mw 113}Constante de Chaitin¹³⁹

{\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 }

Ver también: Problema de la parada TA100264[0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1]19750.0078749969978123844 2,80777 02420 28519 36522 ^{Mw 114}Constante Fransén–Robinson ¹⁴⁰

{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)}]A058655[2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...]19782.80777024202851936522150118655777293 1,01734 30619 84449 13971 ^{Mw 115}Zeta(6) ¹⁴¹

\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}} ...

\textstyle = \sum_{n=1}^\infty\frac{{1}}{n^6} = \frac{1}{1^6} + \frac{1}{2^6} + \frac{1}{3^6} + \frac{1}{4^6} + \frac{1}{5^6} + ...

Prod[n=1 to ∞]
{1/(1
-prime(n)^-6)}TA013664[1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...]1.01734306198444913971451792979092052 1,64872 12707 00128 14684 ^{Ow 5}Raíz cuadrada delnúmero e ¹⁴²

\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!)}TA019774[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∈ℕ1.64872127070012814684865078781416357 i ... ^{Mw 116} Número imaginario¹⁴³

{i}

\sqrt{-1} = \frac{\ln(-1)}{\pi} \qquad\qquad \mathrm{e}^{i\,\pi} = -1

sqrt(-1)C I1501
à
1576 i 4,81047 73809 65351 65547Constante de John ¹⁴⁴

\gamma

\sqrt[i]{i} = i^{-i} = i^{\frac{1}{i}} = (i^i)^{-1} = e^{\frac{\pi}{2}}

e^(π/2)TA042972[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,...]4.81047738096535165547303566670383313 0.49801 56681 18356 04271

0.15494 98283 01810 68512 i

Factorial de i¹⁴⁵

{i}\,!

\Gamma (1+i) = i \, \Gamma (i) = \int\limits_0^\infty \frac{t^i}{e^t} \mathrm{d} t

Gamma(1+i)CA212877
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,...] i0.49801566811835604271369111746219809
- 0.15494982830181068512495513048388 i 0,43828 29367 27032 11162

0,36059 24718 71385 485 i ^{Mw 117}

Tetración infinita de i¹⁴⁶

{}^\infty {i}

\lim_{n \to \infty} {}^n i = \lim_{n \to \infty} \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n

i^i^i^...CA077589
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...] i0.43828293672703211162697516355126482
+ 0.36059247187138548595294052690600 i 0,56755 51633 06957 82538Módulo de la
Tetración infinita dei¹⁴⁷

|{}^\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,...]0.56755516330695782538461314419245334 0,26149 72128 47642 78375 ^{Mw 118}Constante de Meissel-Mertens ¹⁴⁸

{M}

\lim_{n \rightarrow \infty } \!\! \left( \sum_{p \leq n} \frac{1}{p} \! - \ln(\ln(n))\! \right) \!\! = \underset{\!\!\!\! \gamma: \, \text{Constante de Euler} ,\,\, p: \, \text{primo}}{\! \gamma \! + \!\! \sum_{p} \!\left( \! \ln \! \left( \! 1 \! - \! \frac{1}{p} \! \right) \!\! + \! \frac{1}{p} \! \right)}

gamma+
Sum[n=1 to ∞]
{ln(1-1/prime(n))
+1/prime(n)}A077761[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...]1866
y
18730.26149721284764278375542683860869585 1,92878 00... ^{Mw 119}Constante de Wright¹⁴⁹

{\omega}

\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]1.9287800.. 0,37395 58136 19202 28805 ^{Mw 120}Constante de Artin ¹⁵⁰

{C}_{Artin}

\prod_{n=1}^{\infty} \left(1-\frac{1}{p_n(p_n-1)}\right)\quad p_n \scriptstyle \text{ = primos}

Prod[n=1 to ∞]
{1-1/(prime(n)
(prime(n)-1))}A005596[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]19990.37395581361920228805472805434641641 4,66920 16091 02990 67185 ^{Mw 121}Constante δ de Feigenbaum δ ¹⁵¹

{\delta}

\lim_{n \to \infty}\frac {x_{n+1}-x_n}{x_{n+2}-x_{n+1}} \qquad \scriptstyle x \in (3,8284;\, 3,8495)

\scriptstyle x_{n+1}=\,ax_n(1-x_n)\quad {o} \quad x_{n+1}=\,a\sin(x_n)

A006890[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]19754.66920160910299067185320382046620161 2,50290 78750 95892 82228 ^{Mw 122}Constante α de Feigenbaum ¹⁵²

\alpha

\lim_{n \to \infty}\frac {d_n}{d_{n+1}}

A006891[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]19792.50290787509589282228390287321821578 5,97798 68121 78349 12266 ^{Mw 123}Constante hexagonal Madelung ₂ ¹⁵³

{H}_{2}(2)

\pi \ln(3) \sqrt 3

Pi Log[3]Sqrt[3]A086055[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]5.97798681217834912266905331933922774 0,96894 61462 59369 38048Constante Beta(3) ¹⁵⁴

{\beta} (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} {+} ...

Sum[n=1 to ∞]
{(-1)^(n+1)
/(-1+2n)^3}TA153071[0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...]0.96894614625936938048363484584691860 1,90216 05831 04 ^{Mw 124}Constante de Brun ₂
= Σ inverso
primos gemelos ¹⁵⁵

{B}_{\,2}

\textstyle \underset{p,\, p+2: \, {primos}}{\sum (\frac1{p}+\frac1{p+2})} = (\frac1{3} {+} \frac1{5}) + (\tfrac1{5} {+} \tfrac1{7}) + (\tfrac1{11} {+} \tfrac1{13}) + ...

N[prod[n=2 to 0,870∞]
[1-1/(prime(n)
-1)^2]]A065421[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]19191.90216058310 0,87058 83799 75 ^{Mw 125}Constante de Brun ₄
= Σ inverso
primos gemelos ¹⁵⁶

{B}_{\,4}

\underset{p,\, p+2,\, p+4,\, p+6: \, {primos}} {\left(\tfrac1{5} + \tfrac1{7} + \tfrac1{11} + \tfrac1{13}\right)}+ \left(\tfrac1{11} + \tfrac1{13} + \tfrac1{17} + \tfrac1{19}\right)+ \dots

A213007[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]19190.87058837997 22,45915 77183 61045 47342pi^e ¹⁵⁷

\pi^{e}

\pi^{e}

pi^eA059850[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]22.4591577183610454734271522045437350 3,14159 26535 89793 23846 ^{Mw 126}Número π, constante de Arquímedes ¹⁵⁸·¹⁵⁹

{\pi}

\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)}TA000796[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]-250 ~3.14159265358979323846264338327950288 0,28878 80950 86602 42127 ^{Mw 127}Flajolet and Richmond¹⁶⁰

{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) ...

prod[n=1 to ∞]
{1-1/2^n}A048651[0;3,2,6,4,1,2,1,9,2,1,2,3,2,3,5,1,2,1,1,6,1,...]19920.28878809508660242127889972192923078 0,06598 80358 45312 53707 ^{Mw 128}Límite inferior deTetración ¹⁶¹

{e}^{-e}

\left(\frac {1}{e}\right)^e

1/(e^e)A073230[0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...]0.06598803584531253707679018759684642 0,20787 95763 50761 90854 ^{Mw 129}i^i ¹⁶²

{i}^{i}

e^ \frac{-\pi}{2}

e^(-pi/2)TA049006[0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...]17460.20787957635076190854695561983497877 0,31830 98861 83790 67153 ^{Mw 130}Inverso de Pi,Ramanujan¹⁶³

\frac{1}{\pi}

\frac{2\sqrt{2}}{9801} \sum^\infty_{n=0} \frac{(4n)!\,(1103+26390 \; n)}{(n!)^4 \, 396^{4n}}

2 sqrt(2)/9801
*Sum[n=0 to ∞]
{((4n)!/n!^4)*(1103+
26390n)/396^(4n)}TA049541[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]0.31830988618379067153776752674502872 0,63661 97723 67581 34307 ^{Mw 131}

^{Ow 6}

Constante de Buffon¹⁶⁴

Aguja interseca línea

\frac{2}{\pi}

\frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots

Producto de François Viète

2/PiTA060294[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]1540
a
16030.63661977236758134307553505349005745 0,47494 93799 87920 65033 ^{Mw 132}Constante deWeierstrass ¹⁶⁵

\sigma(\tfrac12)

\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)A094692[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...]1872 ?0.47494937998792065033250463632798297 0,57721 56649 01532 86060 ^{Mw 133}Constante de Euler-Mascheroni¹⁶⁶

{\gamma}

\sum_{n=1}^\infty \sum_{k=0}^\infty \frac{(-1)^k}{2^n+k} \! = \!\sum_{n=1}^\infty \frac{1}{n} -\ln(n) \! = \!\! \int_{0}^{1}\!\! -\ln(\ln \frac{1}{x})\, dx

sum[n=1 to ∞]
|sum[k=0 to ∞]
{((-1)^k)/(2^n+k)}A001620[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,...]17350.57721566490153286060651209008240243 1,70521 11401 05367 76428 ^{Mw 134}Constante de Niven¹⁶⁷

{C}

1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right)

1+ Sum[n=2 to ∞]
{1-(1/Zeta(n))}A033150[1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...]19691.70521114010536776428855145343450816 0,60459 97880 78072 61686 ^{Mw 135}Relación entre el área de un triángulo equilátero y su círculo inscrito.

\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

Serie de Dirichlet Sum[1/(n
Binomial[2 n, n])
, {n, 1, ∞}]TA073010[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...]0.60459978807807261686469275254738524 3,24697 96037 17467 06105 ^{Mw 136}Constante Silver de Tutte–Beraha ¹⁶⁸

\varsigma

2+2 \cos \frac {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)AA116425[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]3.24697960371746706105000976800847962 0,69314 71805 59945 30941 ^{Mw 137}Logaritmo natural de 2

Ln(2)

\sum_{n=1}^\infty \frac{1}{n 2^n} = \sum_{n=1}^\infty \frac{({-}1)^{n+1}}{n} = \frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+{\cdots}

Sum[n=1 to ∞]
{(-1)^(n+1)/n}TA002162[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...]1550
a
16170.69314718055994530941723212145817657 0,66016 18158 46869 57392 ^{Mw 138}Constante de los primos gemelos ¹⁶⁹

{C}_{2}

\prod_{p=3}^\infty \frac{p(p-2)}{(p-1)^2}

prod[p=3 to ∞]
{p(p-2)/(p-1)^2A005597[0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...]19220.66016181584686957392781211001455577 0,66274 34193 49181 58097 ^{Mw 139}Constante límite de Laplace¹⁷⁰

{\lambda}

\frac{ x \; e^\sqrt{x^2+1}}{\sqrt{x^2+1}+1} = 1

(x e^sqrt(x^2+1))
/(sqrt(x^2+1)+1)
= 1A033259[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...]1782 ~0.66274341934918158097474209710925290 0,28016 94990 23869 13303 ^{Mw 140}Constante de Bernstein¹⁷¹

{\beta}

\frac {1}{2\sqrt {\pi}}

1/(2 sqrt(pi))TA073001[0;3,1,1,3,9,6,3,1,3,14,34,2,1,1,60,2,2,1,1,...]19130.28016949902386913303643649123067200 0,78343 05107 12134 40705 ^{Mw 141}Sophomore's Dream₁Johann Bernoulli ¹⁷²

{I}_{1}

\int_0^1 \! x^{-x}\,dx = \sum_{n = 1}^\infty \frac{(-1)^{n+1}}{n^n} = \frac{1}{1^1} - \frac{1}{2^2} + \frac{1}{3^3} - {\cdots}

Sum[n=1 to ∞]
{-(-1)^n /n^n}A083648[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...]16970.78343051071213440705926438652697546 1,29128 59970 62663 54040 ^{Mw 142}Sophomore's Dream ₂Johann Bernoulli¹⁷³

{I}_{2}

\int_0^1 \! \frac{1}{x^x}\, dx = \sum_{n = 1}^\infty \frac{1}{n^n} = \frac{1}{1^1} + \frac{1}{2^2} + \frac{1}{3^3} + \frac{1}{4^4}+ \cdots

Sum[n=1 to ∞]
{1/(n^n)}A073009[1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...]16971.29128599706266354040728259059560054 0,82246 70334 24113 21823 ^{Mw 143}Constante Nielsen-Ramanujan¹⁷⁴

\frac{{\zeta}(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} {-} ...

Sum[n=1 to ∞]
{((-1)^(n+1))/n^2}TA072691[0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...]19090.82246703342411321823620758332301259 0,78539 81633 97448 30961 ^{Mw 144}Beta(1) ¹⁷⁵

{\beta}(1)

\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 to ∞]
{(-1)^n/(2n+1)}TA003881[0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,...]1805
a
18590.78539816339744830961566084581987572 0,91596 55941 77219 01505 ^{Mw 145}Constante de Catalan¹⁷⁶ ¹⁷⁷ ¹⁷⁸

{C}

\int_0^1 \!\! \int_0^1 \!\! \frac{1}{1{+}x^2 y^2}\, dx \,dy = \! \sum_{n = 0}^\infty \! \frac{(-1)^n}{(2n{+}1)^2} \! = \! \frac{1}{1^2}{-}\frac{1}{3^2}{+}{\cdots}

Sum[n=0 to ∞]
{(-1)^n/(2n+1)^2}T ?A006752[0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...]18640.91596559417721901505460351493238411 1,05946 30943 59295 26456 ^{Ow 7}Intervalo entre semitonos de laescala musical ¹⁷⁹ ¹⁸⁰

\sqrt[12]{2}

\scriptstyle 440\, Hz. \textstyle 2^\frac{1}{12} \, 2^\frac{2}{12} \, 2^\frac{3}{12} \, 2^\frac{4}{12} \, 2^\frac{5}{12} \, 2^\frac{6}{12} \, 2^\frac{7}{12} \, 2^\frac{8}{12} \, 2^\frac{9}{12} \, 2^\frac{10}{12} \, 2^\frac{11}{12} \, 2

\scriptstyle {\color{white}...\color{black} Do_1\;\; Do\#\;\, Re\;\, Re\#\;\, Mi\;\; Fa\;\; Fa\#\; Sol\;\, Sol\#\, La\;\; La\#\;\; Si\;\, Do_2}

\scriptstyle {\color{white}....\color{black}C_1\;\;\;\; C\#\;\;\;\, D\;\;\; D\#\;\;\, E\;\;\;\;\, F\;\;\;\, F\#\;\;\; G\;\;\;\; G\#\;\;\; A\;\;\;\, A\#\;\;\;\, B\;\;\; C_2}

2^(1/12)AA010774[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]1.05946309435929526456182529494634170 1,13198 82487 943 ^{Mw 146}Constante de Viswanath ¹⁸¹

{C}_{Vi}

\lim_{n \to \infty}|a_n|^\frac{1}{n}

donde a_n = Sucesión de Fibonaccilim_(n->∞)
|a_n|^(1/n)T ?A078416[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]19971.1319882487943 ... 1,20205 69031 59594 28539 ^{Mw 147}Constante de Apéry¹⁸²

\zeta(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=

\frac{1}{2} \sum_{n=1}^\infty \frac{H_n}{n^2} = \frac{1}{2} \sum_{i=1}^\infty \sum_{j=1}^\infty \frac{1}{ij(i{+}j)}= \!\!\int \limits_0^1 \!\!\int \limits_0^1 \!\!\int \limits_0^1 \frac{\mathrm{d}x \mathrm{d}y \mathrm{d}z}{1 - xyz}

Sum[n=1 to ∞]
{1/n^3}IA010774[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...]19791.20205690315959428539973816151144999 1,22541 67024 65177 64512 ^{Mw 148}Gamma(3/4) ¹⁸³

\Gamma(\tfrac34)

\left(-1+\frac{3}{4}\right)! = \left(-\frac{1}{4}\right)!

(-1+3/4)!A068465[1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,...]1.22541670246517764512909830336289053 1,23370 05501 36169 82735 ^{Mw 149}Constante de Favard¹⁸⁴

\tfrac34\zeta(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)}TA111003[1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...]1902
a
19651.23370055013616982735431137498451889 1,25992 10498 94873 16476 ^{Mw 150}Raíz cúbica de dos, constante Delian

\sqrt[3]{2}

\sqrt[3]{2}

2^(1/3)AA002580[1;3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3,...]1.25992104989487316476721060727822835 9,86960 44010 89358 61883Pi al Cuadrado

{\pi} ^2

6 \zeta(2) = 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}TA002388[9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,...]9.86960440108935861883449099987615114 1,41421 35623 73095 04880 ^{Mw 151}Raíz cuadrada de 2, constante dePitágoras ¹⁸⁵

\sqrt{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)}AA002193[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]
= [1;2...]< -8001.41421356237309504880168872420969808 262 53741 26407 68743
,99999 99999 99250 073 ^{Mw 152}Constante de Hermite-Ramanujan ¹⁸⁶

{R}

e^{\pi\sqrt{163}}

e^(π sqrt(163))TA060295[262537412640768743;1,1333462407511,1,8,1,1,5,...]1859262537412640768743.999999999999250073 0,76159 41559 55764 88811 ^{Mw 153}Tangente hiperbólicade 1 ¹⁸⁷

{th} \, 1

\frac{e-\frac{1}{e}}{e+\frac{1}{e}} = \frac{e^2-1}{e^2+1}

(e-1/e)/(e+1/e)TA073744[0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...]
= [0;2p+1], p∈ℕ0.76159415595576488811945828260479359 0,36787 94411 71442 32159 ^{Mw 154}Inverso del Número e¹⁸⁸

\frac{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!}TA068985[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...]
= [0;2,1,1,2p,1], p∈ℕ16180.36787944117144232159552377016146086 1,53960 07178 39002 03869 ^{Mw 155}Constante Square Ice de Lieb ¹⁸⁹

{W}_{2D}

\lim_{n \to \infty}(f(n))^{n^{-2}}=\left(\frac{4}{3}\right)^\frac{3}{2} = \frac{8 \sqrt{3}}{9}

(4/3)^(3/2)AA118273[1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...]19671.53960071783900203869106341467188655 7,38905 60989 30650 22723Constante cónica de Schwarzschild ¹⁹⁰

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!}TA072334[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.7.38905609893065022723042746057500781 1,44466 78610 09766 13365 ^{Mw 156}Número de Steiner ¹⁹¹

\sqrt[e]{e}

e^{1/e}

Límite superior de Tetración e^(1/e)A073229[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]1796
a
18631.44466786100976613365833910859643022 4,53236 01418 27193 80962Constante 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)A163973[4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...]4.53236014182719380962768294571666681 1,57079 63267 94896 61923 ^{Mw 157}Constante de Favard K1
Producto de Wallis ¹⁹²

{\frac{\pi}{2}}

\prod_{n=1}^{\infty} \left(\frac{4n^2}{4n^2 - 1}\right) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots

Prod[n=1 to ∞]
{(4n^2)/(4n^2-1)}A019669[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...]16551.57079632679489661923132169163975144 1,61803 39887 49894 84820 ^{Mw 158}Fi, Número áureo ¹⁹³ ·¹⁹⁴

{\varphi}

\frac{1 + \sqrt{5}}{2} = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}}

(1+5^(1/2))/2AA001622[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...]
= [0;1,...]-300 ~1.61803398874989484820458633436563812 1,64493 40668 48226 43647 ^{Mw 159}Función Zeta (2) de Riemann

{\zeta}(\,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}TA013661[1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...]1826
a
18661.64493406684822643647241516664602519 1,73205 08075 68877 29352 ^{Mw 160}Constante de Theodorus¹⁹⁵

\sqrt{3}

\sqrt[3]{3 \,\sqrt[3]{3 \, \sqrt[3]{3 \,\sqrt[3]{3 \,\sqrt[3]{3 \,\cdots}}}}}

(3(3(3(3(3(3(3)
^1/3)^1/3)^1/3)
^1/3)^1/3)^1/3)
^1/3 ...AA002194[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...]
= [1;1,2,...]-465
a
-3981.73205080756887729352744634150587237 1,75793 27566 18004 53270 ^{Mw 161}Número de Kasner ¹⁹⁶

{R}

\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,...]1878
a
19551.75793275661800453270881963821813852 2,29558 71493 92638 07403 ^{Mw 162}Constante universal parabólica ¹⁹⁷

{P}_{\,2}

\ln(1 + \sqrt2) + \sqrt2 \; = \; \operatorname{arcsinh}(1)+\sqrt{2}

ln(1+sqrt 2)+sqrt 2TA103710[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...]2.29558714939263807403429804918949038 3,30277 56377 31994 64655 ^{Mw 163}Número de bronce ¹⁹⁸

{\sigma}_{\,Rr}

\frac {3+\sqrt{13}}{2} = 1+\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}}

(3+sqrt 13)/2AA098316[3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...]
= [3;3,...]3.30277563773199464655961063373524797 2,37313 82208 31250 90564Constante de Lévy ₂¹⁹⁹

2\,ln\,\gamma

\frac{\pi^2}{6ln(2)}

Pi^(2)/(6*ln(2))TA174606[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]19362.37313822083125090564344595189447424 2,50662 82746 31000 50241Raíz cuadrada de 2 pi

\sqrt{2 \pi}

\sqrt{2 \pi} = \lim_{n \to \infty} \frac {n! \; e^n}{n^n \sqrt{n}}{\color{white}....\color{black}}

Fórmula de Stirlingsqrt (2*pi)TA019727[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]1692
a
17702.50662827463100050241576528481104525 2,66514 41426 90225 18865 ^{Mw 164}Constante de Gelfond-Schneider ²⁰⁰

G_{\,GS}

2^{\sqrt{2}}

2^sqrt{2}TA007507[2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...]19342.66514414269022518865029724987313985 2,68545 20010 65306 44530 ^{Mw 165}Constante de Khinchin²⁰¹

K_{\,0}

\prod_{n=1}^\infty \left[{1{+}{1\over n(n{+}2)}}\right]^\frac{\ln n}{\ln 2} = \lim_{n \to \infty } \left( \prod_{k=1}^n a_k \right) ^\frac{1}{n}

... donde a_k son elementos de la fracción continua [a₀; a₁, a₂, a₃, ...]prod[n=1 to ∞]
{(1+1/(n(n+2)))
^((ln(n)/ln(2))}TA002210[2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...]19342.68545200106530644530971483548179569 3,27582 29187 21811 15978 ^{Mw 166}Constante de Khinchin-Lévy ²⁰² · ²⁰³

\gamma

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,...]19363.27582291872181115978768188245384386 3,35988 56662 43177 55317 ^{Mw 167}Constante de Prévost, sum. inversos deFibonacci ²⁰⁴

\Psi

\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

IA079586[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]19773.35988566624317755317201130291892717 1,32471 79572 44746 02596 ^{Mw 168}Número plástico ²⁰⁵

{\rho}

\sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \cdots}}}}

AA060006[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...]19291.32471795724474602596090885447809734 4,13273 13541 22492 93846Raíz de 2 e pi

\sqrt{2e \pi}

\sqrt{2e \pi}

sqrt(2e pi)A019633[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]4.13273135412249293846939188429985264 2,66514 41426 90225 18865 ^{Mw 169}Constante de Gelfond²⁰⁶

{e}^{\pi}

(-1)^{-i} = i^{-2i} = \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2!} + \frac{\pi^{3}}{3!} + \cdots

Sum[n=0 to ∞]
{(pi^n)/n!}TA039661[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]1906
a
196823.1406926327792690057290863679485474

Tabla de constantes matemáticas[editar]

Abreviaciones usadas:

0	0	cero	R	-	-
1	1	uno	R	-	-
2	2	dos	R	-	-
0	1- ∞(e^ipi2n÷x^½)= 0	se cumple ∀ n ≥1 y ∀ x ≥1. ∞ indica la tetración infinita de la forma encerrada	R	-	2013
$\pi\,$	3,14159 26535 89793 23846 26433 83279 50288 41971	Pi, constante deArquímedeso número deLudolph	T	10.000.000.000.050²⁰⁷	22/10/2011
$e=\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n$	2,71828 18284 59045 23536 02874 71352 66249 77572	Constante de Napier, base dellogaritmo natural	T	1.000.000.000.000²⁰⁸²⁰⁹	2010
$\sqrt{2}$	1,41421 35623 73095 04880 16887 24209 69807 85696	Raíz cuadrada de dos, constante dePitágoras.	I	1.000.000.000.000²⁰⁹	2010
$\sqrt{3}$	1,73205 08075 68877 29352 74463 41505 87236 69428	Raíz cuadrada de tres	I	10.000.000
$\sqrt{5}$	2,23606 79774 99789 69640 91736 68731 27623 54406	Raíz cuadrada de cinco	I	10.000.000²¹⁰	20/12/1999
$\phi,\tau = \frac{1+\sqrt{5}}{2}$	1,61803 39887 49894 84820 45868 34365 63811 77203	Número áureo, simbolizado tanto como φ como por τ.	I	1.000.000.000.000²⁰⁹	2010
$\gamma = \lim_{n \rightarrow \infty } \left[\sum_{k=1}^n \frac{1}{k} - \ln(n) \right]$	0,57721 56649 01532 86060 65120 90082 40243 10421	Constante de Euler-Mascheroni	?	29.844.489.545²⁰⁹	2009
$\alpha\,$	-2,50290 78750 95892 82228 39028 73218 21578 63812	Constante α de Feigenbaum		1018²¹¹	1999
$\delta\,$	4,66920 16091 02990 67185 32038 20466 20161 72581	Constante δ de Feigenbaum		1018²¹¹	1999
$C_{artin}=\prod_{p\, primo}\left(1-\frac{1}{p(p-1)}\right)$	0,37395 58136 19202 28805 47280 54346 41641 51116	Constante de Artin		1000²⁰⁹	1999
$C_2=\prod_{p\ge 3}\frac{p(p-2)}{(p-1)^2}$	0,66016 18158 46869 57392 78121 10014 55577 84326	Constante de los primos gemelos		5.020²⁰⁹	2001
$B_2\,$	1,90216 0582	Constante de Brunpara los primos gemelos		9²⁰⁹	1999 / 2002