Constantes matemáticas: definición, ejemplos y propiedades

Nombre

Símbolo

Valor

Significado

Pi, la constante de Arquímedes o el número de Ludoph

π

≈3.141592653589793

Número trascendental que es la relación entre la longitud de la circunferencia de un círculo y su diámetro. También es el área del círculo unitario.

E, la constante de Napier o el número de Euler (pronunciado "oilers")

e

≈2.718281828459045

Un número trascendental que es la base de los logaritmos naturales, a veces llamado "número natural".

Relación áurea

φ

5 + 1 2 ≈ 1,618 {\displaystyle {\frac {{sqrt {5}}+1}{2}}approx 1,618}

Es el valor de un valor mayor dividido por un valor menor si éste es igual al valor de la suma de los valores dividido por el valor mayor.

Raíz cuadrada de 2, constante de Pitágoras

2 {\displaystyle {\sqrt {2}}

≈ 1.414 {\a6)

Un número irracional que es la longitud de la diagonal de un cuadrado con lados de longitud 1. Este número no se puede escribir como una fracción.

Valor

Nombre

Símbolo

LaTeX

Fórmula

Tipo

OEIS

Fracción continua

3.24697960371746706105000976800847962

Plata, Tutte-Beraha constante

ς {\displaystyle \varsigma }

2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 7 + 7 7 + ⋯ 3 3 3 1 + 7 + 7 7 + 7 7 + ⋯ 3 3 3 {\displaystyle 2+2\cos(2\pi /7)=\textstyle 2+{{frac}{2+{sqrt[{3}]{7+7{sqrt[{3}]{7+7{sqrt[{3}]{\,7+\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 de París

C P a {\displaystyle C_{Pa}}

∏ n = 2 ∞ 2 φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{infty }{frac {2\varphi }{varphi +\varphi _{n}};,\varphi ={Fi}}.

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

El radical anidado de Ramanujan R₅

R 5 {\displaystyle R_{5}}

5 + 5 + 5 - 5 + 5 + 5 - ⋯ = 2 + 5 + 15 - 6 5 2 {\displaystyle \scriptstyle {\sqrt {5+{sqrt}{5+{sqrt}{5-{sqrt}{5+{sqrt}{5+{sqrt}{5+{sqrt}{5-{sqrt}{5}{sqrt}{5}{sqrt}{sqrt}{5}};=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 cuadrada de 5, suma de Gauss

5 {\displaystyle {\sqrt {5}}

∀ n = 5 , ∑ k = 0 n - 1 e 2 k 2 π i n = 1 + e 2 π i 5 + e 8 π i 5 + e 18 π i 5 + e 32 π i 5 {\displaystyle \scriptstyle \forall \,n=5,\displaystyle \\\\Nsuma _{k=0}^{n-1}e^{\\Nfrac {2k^{2}\pi i}{n}=1+e^{\frac {2\pi i}{5}+e^{\\Nfrac {8\pi i}{5}+e^{\Nfrac {18\pi i}{5}+e^{\Nfrac {32\pi i}{5}}

Sum[k=0 a 4]{e^(2k^2 pi i/5)}

I

A002163

[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...]
= [2;(4),...]

3.62560990822190831193068515586767200

Gamma(1/4)

Γ ( 1 4 ) {\displaystyle \Gamma ({\tfrac {1}{4}})}

¡4 ( 1 4 ) ! ¡= ( - 3 4 ) ! {\displaystyle 4\\a izquierda({\frac {1}{4}{directo)!=\a izquierda(-{\frac {3}{4}{directo)!}

¡4(1/4)!

T

A068466

[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]

0.18785964246206712024851793405427323

MRB constante, Marvin Ray Burns

C M R B {\displaystyle C_{MRB}}

∑ n = 1 ∞ ( - 1 ) n ( n 1 / n - 1 ) = - 1 1 + 2 2 - 3 3 + 4 4 ... {{displaystyle \\\}suma _{n=1}^{infty }({-}1)^{n}(n^{1/n}{-}1)=-{{sqrt[{1}]{1}+{{sqrt[{2}]{2}}+{{sqrt[{3}]{3}}+{{sqrt[{4}]{4}{,\dots }

Sum[n=1 a ∞]{(-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

ρ {\displaystyle {\rho }}

∏ n = 3 ∞ cos ( π n ) = cos ( π 3 ) cos ( π 4 ) cos ( π 5 ) ... {\displaystyle \\\n=3}^{{infty }\cos \left({\frac {\pi }{n}}right)=\cos \left({\frac {\pi }{3}{right)\ncos \left({\frac {\pi }{4}{right)\ncos \left({\frac {\pi }{5}{right)\n}

prod[n=3 a ∞]{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

Función Exp(gamma)
G-Barnes

e γ {\displaystyle e^{\gamma }}

∏ n = 1 ∞ e 1 n 1 + 1 n = ∏ n = 0 ∞ ( ∏ k = 0 n ( k + 1 ) ( - 1 ) k + 1 ( n k ) ) 1 n + 1 = {\displaystyle \{prod _{n=1}^{infty }{{frac {e^{frac {1}{n}}}{1+{\tfrac {1}{n}}}}=prod _{n=0}^{infty }{left(\{prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \\\_}right)^{{frac {1}{n+1}=}

( 2 1 ) 1 / 2 ( 2 2 1 ⋅ 3 ) 1 / 3 ( 2 3 ⋅ 4 1 ⋅ 3 3 ) 1 / 4 ( 2 4 ⋅ 4 4 1 ⋅ 3 6 ⋅ 5 ) 1 / 5 ... {\displaystyle \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}} {directo)^{1/4} {puntos a la izquierda({frac {2^{4}{cdot 4^{4}{1\cdot 3^{6}{cdot 5}} {directo)^{1/5}

Prod[n=1 a ∞]{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 {\displaystyle {A}}

e 1 12 - ζ ′ ( - 1 ) = e 1 8 - 1 2 ∑ n = 0 ∞ 1 n + 1 ∑ k = 0 n ( - 1 ) k ( n k ) ( k + 1 ) 2 ln ( k + 1 ) {\displaystyle e^{{frac {1}{12}}-\zeta ^{{prime }(- 1)1)}=e^{{frac {1}{8}}-{{frac {1}{2}}suma \Nde los límites _{n=0}^{infty}}{{frac {1}{n+1}}suma \Nde los límites _{k=0}^{n}{izquierda(-1\a la derecha)^{k}{binom {n}{k}{izquierda(k+1\a la derecha)^{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 cónica de Schwarzschild

e 2 {\displaystyle e^{2}}

¡∑ n = 0 ∞ 2 n n ! ¡= 1 + 2 + 2 2 2 ! ¡+ 2 3 3 ! ¡+ 2 4 4 ! ¡+ 2 5 5 ! + ... {\displaystyle \ {{n=0}^{infty }{{2^{n}{n!}}=1+2+{frac {2^{2}{2!}}+{frac {2^{3}{3!}}+{frac {2^{4}{4!}+{frac {2^{5}{5!}}+{puntos}

Suma[n=0 a ∞]{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 de Gieseking

G G i {\displaystyle {G_{Gi}}

3 3 4 ( 1 - ∑ n = 0 ∞ 1 ( 3 n + 2 ) 2 + ∑ n = 1 ∞ 1 ( 3 n + 1 ) 2 ) = {\displaystyle {\frac {3{cuadro {3}}{4}\left(1-)\\N - suma _{n=0}^{infty }{frac {1}(3n+2)^{2}}+{suma _{n=1}^{infty }{frac {1}(3n+1)^{2}} {directo)=}

3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± ... ) {\displaystyle \textstyle {\frac {3{sqrt {3}}{4}left(1-{frac {1}{2^{2}}+{frac {1}{4^{2}}-{frac {1}{5^{2}}+{frac {1}{8^{2}}+{frac {1}{10^{2}}pm \dots \right)} .

T

A143298

[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]

2.62205755429211981046483958989111941

Lemniscata constante

ϖ {\displaystyle {\varpi }}

π G = 4 2 π ( 1 4 ! ) 2 {\displaystyle \pi \\\},{G}=4{{sqrt {\tfrac {2}{\pi }},({\tfrac {1}{4}})^{2}}

4 sqrt(2/pi) (1/4!)^2

T

A062539

[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]

0.83462684167407318628142973279904680

Constante de Gauss

G {\displaystyle {G}}

¡1 a g m ( 1 , 2 ) = 4 2 ( 1 4 ! ) 2 π 3 / 2 A g m : A r i t h m e t i c - g e o m e t r i c m e n t e {{displaystyle}} {{Agm:\};Aritmética-geométrica{{};media}{{frac {1}{mathrm {agm} (1,{\sqrt {2})}}={{frac {4{sqrt {2}},({\tfrac {1}{4}}!)^{2}}{pi ^{3/2}}}}}}

(4 sqrt(2)(1/4!)^2)/pi^(3/2)

T

A014549

[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]

1.01734306198444913971451792979092052

Zeta(6)

ζ ( 6 ) {\a6)

π 6 945 = ∏ n = 1 ∞ 1 1 - p n - 6 p n : p r i m o = 1 1 - 2 - 6 ⋅ 1 1 - 3 - 6 ⋅ 1 1 - 5 - 6 . . . {\displaystyle {\frac {\pi ^{6}}{945}=\prod _{n=1}^{{infty}}{{p_{n}}:\{{primo}} {{frac}{1}{p_{n}^-6}}={{frac}{1{-}2^{-6}} {{cdot}} {{frac}{1}{-}3^{-6}} {{cdot}} {{1}{-}5^{-6}}...}

Prod[n=1 a ∞] {1/(1-ésimo(n)^-6)}

T

A013664

[1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...]

0,60792710185402662866327677925836583

Constante de Hafner-Sarnak-McCurley

1 ζ ( 2 ) {\displaystyle {\frac {1}{zeta (2)}}

6 π 2 = ∏ n = 0 ∞ ( 1 - 1 p n 2 ) p n : p r i m o = ( 1 - 1 2 2 ) ( 1 - 1 3 2 ) ( 1 - 1 5 2 ) ... {\displaystyle {\frac {6}{pi ^{2}}=}prod _{n=0}^{\infty }{{p_{n}}:\{{primo}} {Izquierda(1-{frac {1}{p_{n}^2}}Derecha)}}=}textstyle {Izquierda(1{-}{frac {1}{2^2}}Derecha)}{Izquierda(1{-}{frac {1}{3^{2}}Derecha)}{{{puntos}}}

Prod{n=1 a ∞} (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

La relación entre un cuadrado y los círculos circunscritos o inscritos

π 2 2 {\displaystyle {\frac {\pi }{2{sqrt {2}}}}}

∑ n = 1 ∞ ( - 1 ) ⌊ n - 1 2 ⌋ 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 - ... {\displaystyle \\\Nsum _{n=1}^{infty }{{{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}{puntos}}

suma[n=1 a ∞]{(-1)^(piso((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 Fransén-Robinson

F {\displaystyle {F}}

∫ 0 ∞ 1 Γ ( x ) d x . = e + ∫ 0 ∞ e - x π 2 + ln 2 x d x {\displaystyle \int _{0^{infty }{frac {1}{Gamma (x)}},dx.=e+int _{0}^{infty }{frac {e^{x}}{pi ^{2}+\ln ^{2}}x},dx}

N[int[0 a ∞] {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

Raíz cuadrada del número e

e {\displaystyle {\sqrt {e}}

¡∑ n = 0 ∞ 1 2 n n ! ¡= ∑ n = 0 ∞ 1 ( 2 n ) ! ¡! = 1 1 + 1 2 + 1 8 + 1 48 + ⋯ {\displaystyle \\\Nsum _{n=0}^{{infty }{1}{2^{n}n!}}={sum _{n=0}^{{infty }{{1}{(2n)!!}}={{frac {1}{1}}+{frac {1}{2}}+{frac {1}{8}}+{frac {1}{48}}+\cdots }

suma[n=0 a ∞]{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

Número imaginario

i {\displaystyle {i}

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

sqrt(-1)

C

262537412640768743.999999999999250073

Constante de Hermite-Ramanujan

R {\displaystyle {R}}

e π 163 {\displaystyle e^{pi {\sqrt {163}}}}

e^(π sqrt(163))

T

A060295

[262537412640768743;1,1333462407511,1,8,1,1,5,...]

4.81047738096535165547303566670383313

Juan constante

γ {\año de la pantalla \año de la pantalla \año \año}

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

e^(π/2)

T

A042972

[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,...]

4.53236014182719380962768294571666681

Constante de Van der Pauw

α {\año de la pantalla \año de la pantalla \año de la pantalla \año}

π l n ( 2 ) = ∑ n = 0 ∞ 4 ( - 1 ) n 2 n + 1 ∑ n = 1 ∞ ( - 1 ) n + 1 n = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - ... 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ... {\frac {\pi }{ln(2)}}={frac {{suma _{n=0}^{infty}}{{frac {4(-1)^{n}}{2n+1}}{{suma _{n=1}^{infty}}{(-1)^{n+1}{n}}}}={frac {{4}{1}{-{{frac {4}{3}{+}{frac {4}{5}{-}{frac {4}{7}{+}{frac {4}{9}}-puntos}{frac {1}{1}{-}{frac {1}{2}{+}{frac {1}{3}{-}{frac {1}{4}{+}{puntos}}

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 (1)

t h 1 {\diseño de la pantalla th\,1}

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

(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 la fracción continua

C C F {\displaystyle {C}_{CF}}

J 1 ( 2 ) J 0 ( 2 ) F u n c i ó n J k ( ) B e s e l = ∑ n = 0 ∞ n ! n ! ∑ n = 0 ∞ 1 n ! n ! = 0 1 + 1 1 + 2 4 + 3 36 + 4 576 + ... 1 1 + 1 1 + 1 4 + 1 36 + 1 576 + ... {{displaystyle}} {{conjunto de j_{k}()} {{Bessel}} {{conjunto de funciones}} {{frac {J_{1}(2)}{J_{0}(2)} }}}}={{frac {suma de límites _{n=0}^{{infty}} {{frac {n}{n!¡n!}}{{suma \N de los límites _{n=0}^{{infty}}{{1}{n!n!}}}}={{frac {0}{1}+{frac {1}{1}+{frac {2}{4}+{frac {3}{36}+{frac {4}{576}+puntos}{{frac {1}+{frac {1}{4}+{frac {1}{36}+{puntos}}

(suma {n=0 a inf} n/(n!n!)) /(suma {n=0 a 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

Constante inversa de Napier

1 e {\displaystyle {\frac {1}{e}}

¡∑ n = 0 ∞ ( - 1 ) n n ! ¡= 1 0 ! - ¡- 1 1 ! ¡+ 1 2 ! - ¡- 1 3 ! ¡+ 1 4 ! - ¡- 1 5 ! + ... {\displaystyle \ {{n=0}^{{infty}}={{1)^{n}} {{n!}}={frac {1}{0!}}-{frac {1}{1!}}+{frac {1}{2!}}-{frac {1}{3!}+{frac {1}{4!}}-{frac {1}{5!}+{puntos}}

suma[n=2 a ∞]{(-1)^n/n!}

T

A068985

[0;2,1,1,2,1,1,4,1,1,6,1,8,1,1,10,1,1,12,...]
= [0;2,1,(1,2p,1)], p∈ℕ

2.71828182845904523536028747135266250

Constante de Napier

e {\diseño e}

¡∑ n = 0 ∞ 1 n ! ¡= 1 0 ! ¡+ 1 1 + 1 2 ! ¡+ 1 3 ! ¡+ 1 4 ! ¡+ 1 5 ! + ⋯ {\displaystyle \ {{n=0}^{infty}}={frac {1}{n!}}+{frac {1}{1}+{frac {1}{2!}+{frac {1}{3!}+{frac {1}{4!}+{frac {1}{5!}+{cdots }

Suma[n=0 a ∞]{1/n!}

T

A001113

[2;1,2,1,1,4,1,1,6,1,8,1,1,10,1,1,12,1,...]
= [2;(1,2p,1)], p∈ℕ

0.49801566811835604271369111746219809
- 0.15494982830181068512495513048388 i

Factorial de i

¡i ! {\a6}*Estilo de visualización i\a6}*

Γ ( 1 + i ) = i Γ ( i ) {\displaystyle \Gamma (1+i)=i,\Gamma (i)}

Gamma(1+i)

C

A212877 A212878

[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...]
- [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i

0.43828293672703211162697516355126482
+ 0.36059247187138548595294052690600 i

Infinito
Tetralogía de i

∞ i {{displaystyle}}^{{infty}}

lim n → ∞ n i = lim n → ∞ i i ⋅ i ⏟ n {\displaystyle \lim _{n a \infty }}^{n}i=lim _{n a \infty }\\\\bcipitaje {i^{cdot ^\cdot ^{i}}}}} _{n}}

i^i^i^...

C

A077589 A077590

[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...]
+ [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i

0.56755516330695782538461314419245334

Módulo del
infinito
Tetración de i

| ∞ i | {\displaystyle |{}^{\infty }i|}

lim n → ∞ | n i | = | lim n → ∞ i i ⋅ ⋅ i ⏟ n | {\displaystyle \lim _{n\\\a \infty }left|{^{n}i\a derecha|=\left|\lim _{n\a \infty }{underbrace} {i^{{cdot ^{cdot ^{i}}}}} {{n}}Derecha}}

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 {\diseño M}

lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) {\displaystyle \lim _{n}flecha \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 {\año de la pantalla \año de la pantalla \año de la pantalla \año \año \año \año}

⌊ 2 2 2 ⋅ ⋅ 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{cdot ^{cdot ^2^{omega }}}}}}\rfloor } = primos:  ⌊ 2 ω ⌋ {\displaystyle \left\lfloor 2^{\omega }\right\rfloor } =3, ⌊ 2 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{\omega }\right\rfloor } =13, ⌊ 2 2 2 ω ⌋ {\displaystyle \left\lfloor 2^{2^{\omega }}\right\rfloor } =16381, ... {\displaystyle \dots }

A086238

[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]

0.37395581361920228805472805434641641

Artin constante

C A r t i n {\displaystyle C_{Artin}}

∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \{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 de Feigenbaum δ

δ {\displaystyle {\delta }}

lim n → ∞ x n + 1 - x n x n + 2 - x n + 1 x ∈ ( 3 , 8284 ; 3 , 8495 ) {{displaystyle }lim _{n\a \infty }{frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}qquad \scriptstyle x\in (3,8284;\a,3,8495)}

x n + 1 = a x n ( 1 - x n ) o x n + 1 = a sin ( x n ) {\displaystyle \scriptstyle x_{n+1}=,ax_{n}(1-x_{n})\quad {o}quad x_{n+1}=,a\sin(x_{n})}

T

A006890

[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]

2.50290787509589282228390287321821578

Constante de Feigenbaum α

α {\año de la pantalla \año de la pantalla \año de la pantalla \año}

lim n → ∞ d n d n + 1 {\displaystyle \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 de Madelung hexagonal ₂

H 2 ( 2 ) {\displaystyle H_{2}(2)}

π ln ( 3 ) 3 {\displaystyle \pi \ln(3){\aqrt {3}}

Pi Log[3]Sqrt[3]

T

A086055

[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]

0.96894614625936938048363484584691860

Beta(3)

β ( 3 ) {\N-estilo de la pantalla \N-beta (3)}

π 3 32 = ∑ n = 1 ∞ - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + ... {{displaystyle}} {\frac {\pi ^{3}}{32}}=suma _{n=1}^{{infty}}}{{1^{n+1}}(-1+2n)^{3}}={frac {1}{1^{3}}{-}{frac {1}{3^{3}}{+}{frac {1}{5^{3}}{-}{frac {1}{7^{3}}{+}{puntos}}

Suma[n=1 a ∞]{(-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 Brun₂ = Σ primos gemelos inversos

B 2 {\displaystyle B_{\\2}

∑ ( 1 p + 1 p + 2 ) p , p + 2 : p r i m o s = ( 1 3 + 1 5 ) + ( 1 5 + 1 7 ) + ( 1 11 + 1 13 ) + ... {\displaystyle \textstyle \sum {\underset {p,\2:\{{primos}}({\frac {1}{p}+{\frac {1}{p+2}})}}=({\frac {1}{3}{+}{\frac {1}{5}})+({\tfrac {1}{5}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}{+}{\tfrac {1}{13}})+\dots }

A065421

[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]

0.870588379975

Constante de Brun₄ = Σ inversa del primo gemelo

B 4 {\displaystyle B_{,4}}

( 1 5 + 1 7 + 1 11 + 1 13 ) p , p + 2 , p + 4 , p + 6 : p r i m e s + ( 1 11 + 1 13 + 1 17 + 1 19 ) + ... {\displaystyle {\underset {p,\2,\4,\6:\{{primas}} {Izquierda({tfrac {1}{5}}+{tfrac {1}{7}}+{tfrac {1}{11}}+{tfrac {1}{13}}Derecha)}+Izquierda({tfrac {1}{11}+{tfrac {1}{13}}+{tfrac {1}{17}+{tfrac {1}{19}}Derecha)+{puntos}}

A213007

[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]

22.4591577183610454734271522045437350

pi^e

π e {\displaystyle \pi ^{e}}

π e {\displaystyle \pi ^{e}}

pi^e

A059850

[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]

3.14159265358979323846264338327950288

Pi, constante de Arquímedes

π {\año de la pantalla \año de la pantalla \año de la pantalla \año}

lim n → ∞ 2 n 2 - 2 + 2 + ⋯ + 2 ⏟ n {\displaystyle \lim _{n\a \infty },2^{n}{sqrt} {2-{sqrt} {2+{sqrt} +{\a} {2+{puntos} {{sqrt} {2}}}}}}}} _{n}}

Sum[n=0 a ∞]{(-1)^n 4/(2n+1)}

T

A000796

[3;7,15,1,292,1,1,1,2,1,3,1,14,...]

0.06598803584531253707679018759684642

e - e {\displaystyle e^{-e}}

e - e {\displaystyle e^{-e}} ... Límite inferior de la 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

i i i {desde el estilo i^{i}}

e - π 2 {\displaystyle 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 {\año de la pantalla \año de la pantalla \año}

1 2 π {\frac {1}{2}{\fracción cuadrática {\pi }}}}}

T

A073001

[0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…]

0.28878809508660242127889972192923078

Flajolet y Richmond

Q {\diseño Q}

∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 2 2 ) ( 1 - 1 2 3 ) ... {\displaystyle \\\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)\n}

prod[n=1 a ∞]{1-1/2^n}

A048651

0.31830988618379067153776752674502872

Inversa de Pi, Ramanujan

1 π {\displaystyle {\frac {1}{pi }}

¡2 2 9801 ∑ n = 0 ∞ ( 4 n ) ! ( 1103 + 26390 n ) ( n ! ) 4 396 4 n {{displaystyle {\frac {2{cuadrado {2}}{9801}} {{suma _{n=0}^{{infty }{{{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 W E {{displaystyle W_{WE}}

e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {\displaystyle {\frac {e^{frac {\pi }{8}} {\sqrt {\pi }} 4*2^{3/4}{{{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 {\año de la pantalla \año de la pantalla \año}

¡W ( 1 ) = ∑ n = 1 ∞ ( - n ) n - 1 n ! = 1 - 1 + 3 2 - 8 3 + 125 24 - ... {\displaystyle W(1)={suma _{n=1}^{{infty }{{frac {(-n)^{n-1}}{n!}}=1{-}1{+}{frac {3}{2}}{{}{frac {8}{3}}{+}{{frac {125}{24}}-puntos }

suma[n=1 a ∞]{(-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

El número de Euler

γ {\año de la pantalla \año de la pantalla \año \año}

- ψ ( 1 ) = ∑ n = 1 ∞ ∑ k = 0 ∞ ( - 1 ) k 2 n + k {\displaystyle -\psi (1)=suma _{n=1}^{\infty }{suma _{k=0}^{\infty }{frac {(-1)^{k}{2^{n}+k}}

suma[n=1 a ∞]|suma[k=0 a ∞]{((-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 {\displaystyle {\frac {\pi }{3{sqrt {3}}}}}

∑ n = 1 ∞ 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 + ⋯ {{displaystyle \\\\}sum _{n=1}^{\infty }{\frac {1}{2n{elegir n}}=1-{{frac {1}{2}}+{frac {1}{4}}-{frac {1}{5}}+{frac {1}{7}}-{frac {1}{8}}+{cdots }

Sum[1/(n Binomio[2 n, n]), {n, 1, ∞}]

T

A073010

[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,...]

0.63661977236758134307553505349005745

2/Pi, François Viète

2 π {\displaystyle {\frac {2}{pi }}

2 2 ⋅ 2 + 2 2 ⋅ 2 + 2 + 2 ⋯ {\displaystyle {\frac {\sqrt {2}{2}{cdot} {\frac {\sqrt {2+{2}{cdot} {\frac {\sqrt {2+{2}{cdot}}

T

A060294

[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]

0.66016181584686957392781211001455577

Constante prima gemela

C 2 {\displaystyle C_{2}}

∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {\displaystyle \{prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}}

prod[p=3 a ∞]{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 de límite de Laplace

λ {\año de la pantalla \año de la cámara}

A033259

[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]

0.69314718055994530941723212145817657

Logaritmo de 2

L n ( 2 ) {\Ndirección Ln(2)}

∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - ⋯ {{displaystyle \\\_sum _{n=1}^{\infty }{{frac {(-1)^{n+1}}{n}={frac {1}}-{frac {1}{2}}+{frac {1}{3}}-{frac {1}{4}}+{frac {1}{5}}{cdots }

Suma[n=1 a ∞]{(-1)^(n+1)/n}

T

A002162

[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...]

0.78343051071213440705926438652697546

El sueño de un estudiante de segundo año₁ J.Bernoulli

I 1 {\displaystyle I_{1}

∑ n = 1 ∞ ( - 1 ) n + 1 n = 1 - 1 2 2 + 1 3 3 - 1 4 4 + 1 5 5 + ... {\displaystyle \{sum _{n=1}^{{infty }{{{1)^{n+1}{n^{n}}=1-{{frac {1}{2^{2}}+{{frac {1}{3^{3}}+{{frac {1}{4^{4}}+{{frac {1}{5^{5}}+{puntos}

Suma[ -(-1)^n /n^n]

T

A083648

[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,...]

0.78539816339744830961566084581987572

Dirichlet beta(1)

β ( 1 ) {\N-estilo de la pantalla \N-beta (1)}

π 4 = ∑ n = 0 ∞ ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - ⋯ {\frac {\pi }{4}}={suma _{n=0}^{\infty }{{frac {(-1)^{n}}{2n+1}}={frac {1}}-{frac {1}{3}}+{frac {1}{5}}-{frac {1}{7}}+{frac {1}{9}}-{cdots }

Sum[n=0 a ∞]{(-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

Vendedor ambulante Nielsen-Ramanujan

ζ ( 2 ) 2 {\displaystyle {\frac {\zeta (2)}{2}}

π 2 12 = ∑ n = 1 ∞ ( - 1 ) n + 1 n 2 = 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\frac {\pi ^{2}}{12}=suma _{n=1}^{infty }{{{1}^{n+1}}{n^{2}}={frac {1}{1^{2}}{-{frac {1}{2^{2}}{+}{frac {1}{3^{2}}{-{frac {1}{4^{2}}{+}{{puntos}}

Suma[n=1 a ∞]{((-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 catalana

C {\año C}

∑ n = 0 ∞ ( - 1 ) n ( 2 n + 1 ) 2 = 1 1 2 - 1 3 2 + 1 5 2 - 1 7 2 + ⋯ {\displaystyle \sum _{n=0}^{\infty }{{frac {(-1)^{n}}(2n+1)^{2}}={frac {1}{1^{2}}-{frac {1}{3^{2}}+{frac {1}{5^{2}}-{frac {1}{7^{2}}+{cdots }

Sum[n=0 a ∞]{(-1)^n/(2n+1)^2}

I

A006752

[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]

1.05946309435929526456182529494634170

Relación de la distancia entre semitonos

2 12 {\displaystyle {\sqrt[{12}]{2}}

2 12 {\displaystyle {\sqrt[{12}]{2}}

2^(1/12)

I

A010774

[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]

1,.08232323371113819151600369654116790

Zeta(04)

ζ 4 {\a6}

π 4 90 = ∑ n = 1 ∞ 1 n 4 = 1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 + 1 5 4 + ... {\frac {\pi ^{4}{90}=suma _{n=1}^{infty}}={frac {1}{n^{4}}={frac {1}{4}+{frac {1}{2^{4}+{frac {1}{3^{4}}+{frac {1}{4^{4}}+{frac {1}{5^{4}}+{puntos}

Suma[n=1 a ∞]{1/n^4}

T

A013662

[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,...]

1.1319882487943 ...

Viswanaths Archivado 2013-04-13 en la Wayback Machine constante

C V i {\displaystyle C_{Vi}}

lim n → ∞ | a n | 1 n {\displaystyle \lim _{n a \infty }|a_{n}|^{frac {1}{n}}

A078416

[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]

1.20205690315959428539973816151144999

Apéry constante

ζ ( 3 ) {\a6)

∑ n = 1 ∞ 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + ⋯ {{displaystyle \\\_sum _{n=1}^{\infty }{\frac {{1}{n^{3}}={{refrac}{1}{1^{3}}+{refrac}{1}{2^{3}}+{refrac}{1}{3^{3}}+{refrac}{4^{3}}+{refrac}{5^{3}}+{cdots},¡\!}

Suma[n=1 a ∞]{1/n^3}

I

A010774

[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,...]

1.22541670246517764512909830336289053

Gamma(3/4)

Γ ( 3 4 ) {\displaystyle \Gamma ({\tfrac {3}{4})}

¡( - 1 + 3 4 ) ! {\displaystyle \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

3 4 ζ ( 2 ) {\displaystyle {\tfrac {3}{4} {zeta (2)}

π 2 8 = ∑ n = 0 ∞ 1 ( 2 n - 1 ) 2 = 1 2 + 1 3 2 + 1 5 2 + 1 7 2 + ... {\displaystyle {\frac {\pi ^{2}}{8}=suma _{n=0}^{{infty }{{1}(2n-1)^{2}}={frac {1}{1^{2}}+{frac {1}{3^{2}}+{frac {1}{5^{2}}+{frac {1}{7^{2}}+{puntos}

suma[n=1 a ∞]{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

Raíz cúbica de 2, constante Delian

2 3 {\displaystyle {\sqrt[{3}]{2}}

2 3 {\displaystyle {\sqrt[{3}]{2}}

2^(1/3)

I

A002580

[1;3,1,5,1,1,4,1,1,8,1,14,1,10,...]

1.29128599706266354040728259059560054

El sueño de un estudiante de segundo año₂ J.Bernoulli

I 2 {\displaystyle I_{2}

∑ n = 1 ∞ 1 n = 1 + 1 2 2 + 1 3 3 + 1 4 4 + 1 5 5 + 1 6 6 + ... {\displaystyle \\\Nsuma _{n=1}^{infty }{{1}{n^{n}}=1+{frac {1}{2^{2}}+{frac {1}{3^{3}}+{frac {1}{4^{4}}+{frac {1}{5^{5}}+{frac {1}{6^{6}}+{puntos}

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

Número de plástico

ρ {\año de la pantalla \año de la pantalla \año}

1 + 1 + 1 + ⋯ 3 3 3 {\displaystyle {{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

Raíz cuadrada de 2, constante de Pitágoras

2 {\displaystyle {\sqrt {2}}

∏ n = 1 ∞ 1 + ( - 1 ) n + 1 2 n - 1 = ( 1 + 1 1 ) ( 1 - 1 3 ) ( 1 + 1 5 ) . . . {\displaystyle \\\n=1}^{\infty }1+{\frac {(-1)^{n+1}{2n-1}}={{{}}Izquierda(1{+}{\frac {1}{1}}Derecha)}{{{}Izquierda(1{}{3}{Derecha)}{{{{1}{5}{Derecha)...}

prod[n=1 a ∞]{1+(-1)^(n+1)/(2n-1)}

I

A002193

[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]
= [1;(2),...]

1.44466786100976613365833910859643022

Número de Steiner

e 1 e {\displaystyle e^\frac {1}{e}}

e 1 / e {\displaystyle e^{1/e}} ... Límite superior de la tetralogía

A073229

[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]

1.53960071783900203869106341467188655

Constante de hielo cuadrado de Lieb

W 2 D {\displaystyle W_{2D}}

lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 {\displaystyle \lim _{n\to \infty }(f(n))^{n^-2}=left({\frac {4}{3}}right)^{\frac {3}{2}}

(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 Wallis

π / 2 {\desde el punto de vista de la visualización \pi /2}

∏ n = 1 ∞ ( 4 n 2 4 n 2 - 1 ) = 2 1 ⋅ 2 3 ⋅ 4 3 ⋅ 4 5 ⋅ 6 5 ⋅ 6 7 ⋅ 8 7 ⋅ 8 9 ⋯ {\displaystyle \prod _{n=1}^{infty }\left({\frac {4n^{2}{4n^{2}-

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 {\displaystyle E_{\\\\año,B}}

∑ n = 1 ∞ 1 2 n - 1 = 1 1 + 1 3 + 1 7 + 1 15 + ⋯ {{displaystyle}{{suma}{n=1}^{infty}}{{frac {1}{2^{n}-1}}={frac {1}{3}+{frac {1}{7}+{frac {1}{15}}+{cdots{,\}}

suma[n=1 a ∞]{1/(2^n-1)}

I

A065442

[1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...]

1.61803398874989484820458633436563812

Phi, proporción áurea

φ {\\Ndejar de ver el estilo \N de la pantalla }

1 + 5 2 = 1 + 1 + 1 + ⋯ {\displaystyle {\frac {1+{cuadrado}}}{2}}={cuadrado}{1+{cuadrado}{1+{cuadrado}{1+{cuadrado}{1+cuadrado}{1+cuadrado}{2}}.

(1+5^(1/2))/2

I

A001622

[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...]
= [0;(1),...]

1.64493406684822643647241516664602519

Zeta(2)

ζ ( 2 ) {\año de la pantalla \año de la pantalla (\año,2)}

π 2 6 = ∑ n = 1 ∞ 1 n 2 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 + ⋯ {\displaystyle {\frac {\pi ^{2}}{6}=\suma {{n=1}^{infty }{{1}{n^2}}={frac {1}{1^2}}+{frac {1}{2^2}}+{frac {1}{3^2}}+{frac {1}{4^2}}+{cdots }

Suma[n=1 a ∞]{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

La constante de recurrencia cuadrática de Somos

σ {\año de la pantalla \año de la pantalla \año}

1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {{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 Teodoro

3 {\displaystyle {\sqrt {3}}

3 {\displaystyle {\sqrt {3}}

3^(1/2)

I

A002194

[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...]
= [1;(1,2),...]

1.75793275661800453270881963821813852

Número de Kasner

R {\diseño de R}

1 + 2 + 3 + 4 + ⋯ {\displaystyle {\sqrt {1+\sqrt {2+\sqrt {3+\sqrt {4+\cdots }}}}}}}}}

A072449

[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]

1.77245385090551602729816748334114518

Constante Carlson-Levin

Γ ( 1 2 ) {\displaystyle \Gamma ({\tfrac {1}{2}})}

¡π = ( - 1 2 ) ! {\displaystyle {\sqrt {\pi }}=\left(-{{frac {1}{2}}right)!}

sqrt (pi)

T

A002161

[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]

2.29558714939263807403429804918949038

Constante parabólica universal

P 2 {\displaystyle P_{{2}}

ln ( 1 + 2 ) + 2 {\displaystyle \ln(1+{cuadrado {2}})+{cuadrado {2}}

ln(1+sqrt 2)+sqrt 2

T

A103710

[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,...]

2.30277563773199464655961063373524797

Número de bronce

σ R r {{desde el punto de vista de la visualización}}

3 + 13 2 = 1 + 3 + 3 + 3 + ⋯ {\displaystyle {\frac {3+{cuadrado}}}{2}}=1+{cuadrado}{3+{cuadrado}{3+cuadrado}{3+cuadrado}{3+cuadrado}{3+cuadrado}{2}}

(3+sqrt 13)/2

I

A098316

[3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...]
= [3;(3),...]

2.37313822083125090564344595189447424

Constante de Lévy₂

2 ln γ {\Ndice 2,\ln \Ngamma }

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

Pi^(2)/(6*ln(2))

T

A174606

[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]

2.50662827463100050241576528481104525

raíz cuadrada de 2 pi

2 π {\displaystyle {\sqrt {2\pi }}

2 π = lim n → ∞ n ! e n n n n {\displaystyle {{sqrt {2\pi }}={lim _{n\to \infty }} {{frac {n!\\};e^{n}}{{sqrt {n}}}}}

sqrt (2*pi)

T

A019727

[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]

2.66514414269022518865029724987313985

Constante de Gelfond-Schneider

G G S {\displaystyle G_{\\\\\\Nde la GS}}

2 2 {\displaystyle 2^{\\\c al cuadrado {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

K 0 {\displaystyle K_{{0}}

∏ n = 1 ∞ [ 1 + 1 n ( n + 2 ) ] ln n / ln 2 {\displaystyle \{prod _{n=1}^{\infty }left[{1+{1 \over n(n+2)}\ right]^{ln n/\ln 2}}.

prod[n=1 a ∞]{(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 {\año de la pantalla \año de la pantalla \año \año}

e π 2 / ( 12 ln 2 ) {\displaystyle e^{pi ^{2}/(12\ln 2)}}

e^(\pi^2/(12 ln(2))

A086702

[3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...]

3.35988566624317755317201130291892717

Constante recíproca de Fibonacci

Ψ {\\Ndice el estilo \N de la pantalla}

∑ n = 1 ∞ 1 F n = 1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1 13 + ⋯ {{displaystyle \\\\_sum _{n=1}^{{infty }{{frac {1}{F_{n}}={{frac}{1}}+{frac}{1}{1}}+{frac}{2}}+{frac}{3}}+{frac}{5}+{frac}{8}+{frac}{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

2 e π {\displaystyle {\sqrt {2e\pi }}

2 e π {\displaystyle {\sqrt {2e\pi }}

sqrt(2e pi)

T

A019633

[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]

6.58088599101792097085154240388648649

Constante de Froda

2 e {\displaystyle 2^{\\\\\}}

2 e {\displaystyle 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

π 2 {\displaystyle \pi ^{2}}

6 ∑ n = 1 ∞ 1 n 2 = 6 1 2 + 6 2 2 + 6 3 2 + 6 4 2 + ⋯ {{displaystyle 6{suma _{n=1}^{infty }}={{frac {1}{n^2}}+{frac {6}{1^2}}+{frac {6}{3^2}}+{frac {6}{4^2}}+{cdots }

6 Suma[n=1 a ∞]{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 {\displaystyle e^{\pi }}

¡∑ n = 0 ∞ π n n ! ¡= π 1 1 + π 2 2 ! ¡+ π 3 3 ! ¡+ π 4 4 ! + ⋯ {\displaystyle \{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 a ∞]{(pi^n)/n!}

T

A039661

[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]