Constante mathematic

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Un constante mathematic es un quantitate que non varia.

Constantes importante[modificar | modificar fonte]

Structura del tabulas[modificar | modificar fonte]

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


Lista de constantes[modificar | modificar fonte]

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

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

Valor Nomine Symbolo LaTeX Formula in texto Tipo OEIS Fraction continue
3,24697960371746706105000976800847962 Constante Silver de Tutte–Beraha  \varsigma  2+2 \cos(2\pi/7)= \textstyle 2+\frac{2+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}{1+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}} 2+2 cos(2Pi/7) T A116425 [3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]
1,09864196439415648573466891734359621 Constante París  C_{Pa}  \prod_{n=2}^\infty \frac{2 \varphi}{\varphi+ \varphi_n}\; , \varphi= {Fi} I A105415 [1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...]
2,74723827493230433305746518613420282 Ramanujan nested radical R5  R_{5} \scriptstyle \sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}}\;=\textstyle\frac{2+\sqrt{5}+\sqrt{15-6\sqrt{5}}}{2} (2+sqrt(5)+sqrt(15-6 sqrt(5)))/2 I [2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]
2,23606797749978969640917366873127624 Raíz de 5, Suma de Gauss  \sqrt{5}  \scriptstyle \forall \, n=5, \displaystyle  \sum_{k=0}^{n-1} e^{\frac{2 k^2 \pi i}{n}} = 1 + e^\frac{2 \pi i} {5} + e^\frac{8 \pi i} {5} + e^\frac{18 \pi i} {5} + e^\frac{32 \pi i} {5} Sum[k=0 to 4]{e^(2k^2 pi i/5)} I A002163 [2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...]
= [2;(4),...]
3,62560990822190831193068515586767200 Gamma(1/4) \Gamma(\tfrac14)  4 \left(\frac{1}{4}\right)! = \left(-\frac{3}{4}\right)! 4(1/4)! T A068466 [3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]
0,18785964246206712024851793405427323 Constante MRB de Marvin Ray Burns  C_{_{MRB}}  \sum_{n=1}^{\infty} ({-}1)^n (n^{1/n}{-}1) =  - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \sqrt[4]{4}\,... Sum[n=1 to ∞]{(-1)^n (n^(1/n)-1)} T A037077 [0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...]
0,11494204485329620070104015746959874 Constante de Kepler–Bouwkamp {\rho}  \prod_{n=3}^\infty \cos\left(\frac\pi n\right) = \cos\left(\frac\pi 3\right) \cos\left(\frac\pi 4\right) \cos\left(\frac\pi 5\right) ... prod[n=3 to ∞]{cos(pi/n)} T A085365 [0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...]
1,78107241799019798523650410310717954 Exp(gamma) función
G-Barnes
e^{\gamma} \prod_{n=1}^\infty \frac{e^{\frac{1}{n}}}{1+\tfrac1n} = \prod_{n=0}^\infty \left(\prod_{k=0}^n (k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac{1}{n+1}} =

\textstyle \left ( \frac{2}{1} \right )^{1/2} \left (\frac{2^2}{1 \cdot 3} \right )^{1/3} \left (\frac{2^3 \cdot 4}{1 \cdot 3^3} \right )^{1/4}
\left (\frac{2^4 \cdot 4^4}{1 \cdot 3^6 \cdot 5} \right )^{1/5}...

Prod[n=1 to ∞]{e^(1/n)}/{1 + 1/n} T A073004 [1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...]
1,28242712910062263687534256886979172 Constante de Glaisher–Kinkelin {A}  e^{\frac{1}{12}-\zeta^{\prime}(-1)} = e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^{\infty} \frac{1}{n+1} \sum\limits_{k=0}^{n} \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)} e^(1/2-zeta´{-1}) T A074962 [1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...]
7,38905609893065022723042746057500781 Constante conica de Schwarzschild e^2  \sum_{n = 0}^\infty \frac{2^n}{n!} = 1+2+\frac{2^2}{2!}+\frac{2^3}{3!}+\frac{2^4}{4!}+\frac{2^5}{5!}+... Sum[n=0 to ∞]{2^n/n!} T A072334 [7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...]
= [7,2,(1,1,n,4*n+6,n+2)], n = 3, 6, 9, etc.
1,01494160640965362502120255427452028 Constante Gieseking {G_{Gi}} \frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)=

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

T A143298 [1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2,62205755429211981046483958989111941 Constante Lemniscata {\varpi}  \pi \, {G} = 4 \sqrt{\tfrac2\pi} \,(\tfrac14 !)^2 4 sqrt(2/pi) (1/4!)^2 T A062539 [2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]
0,83462684167407318628142973279904680 Constante de Gauss {G}   \underset{ agm:\; Media \;aritm\acute{e}tica-geom\acute{e}trica} {\frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{4 \sqrt{2} \,(\tfrac14 !)^2}{\pi ^{3/2}}} (4 sqrt(2)(1/4!)^2)/pi^(3/2) T A014549 [0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]
0,0078749969978123844 Constante de Chaitin {\Omega} \sum_{p \in P} 2^{-|p|} \overset {p: \; {Programa \; que \;se \; para}} \underset{ { P:\; Conjunto \; de \; todos \; los \; programas \; que \; se \; paran.}}
{\scriptstyle  [p]:\; Tama\tilde{n}o \;del\;programa } ? A100264 [0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1]
1,01734306198444913971451792979092052 Constante Zeta(6) \zeta(6) \frac{\pi^6}{945} = \prod_{n=1}^\infty \underset{p_{n}: \, {primo}}\frac{1}{{1-p_n}^{-6}} = \frac{1}{1{-}2^{-6}}{\cdot}\frac{1}{1{-}3^{-6}}{\cdot}\frac{1}{1{-}5^{-6}} ... Prod[n=1 to ∞] {1/(1-ithprime(n)^-6)} T A013664 [1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...]
0,60792710185402662866327677925836583 Constante de Hafner-Sarnak-McCurley \frac{1}{\zeta(2)}  \frac{6}{\pi^2} {=} \prod_{n = 0}^\infty \underset{p_{n}: \, {primo}}{\left(1- \frac{1}{{p_n}^2}\right)}{=}\textstyle  \left(1{-}\frac{1}{2^2}\right)\left(1{-}\frac{1}{3^2}\right)\left(1{-}\frac{1}{5^2}\right)... Prod{n=1 to ∞} (1-1/ithprime(n)^2) T A059956 [0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...]
1,11072073453959156175397024751517342 Razón entre un cuadrado y las círcunferencias ins.o circunscrita \frac{\pi}{2\sqrt 2} \sum_{n = 1}^\infty \frac{(-1)^{\lfloor \frac{n-1}{2}\rfloor}}{2n+1} = \frac{1}{1} + \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \frac{1}{9} + \frac{1}{11} - ... sum[n=1 to ∞]{(-1)^(floor((n-1)/2))/(2n-1)} T A093954 [1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...]
2,80777024202851936522150118655777293 Constante Fransen–Robinson {F} \int_{0}^\infty \frac{1}{\Gamma(x)}\, dx. = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, dx N[int[0 to ∞] {1/Gamma(x)}] T A058655 [2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...]
1,64872127070012814684865078781416357 Raiz cuadrada del numero e \sqrt e \sum_{n = 0}^\infty \frac{1}{2^n n!} = \sum_{n = 0}^\infty \frac{1}{(2n)!!} = \frac{1}{1}+\frac{1}{2}+\frac{1}{8}+\frac{1}{48}+\cdots sum[n=0 to ∞]{1/(2^n n!)} T A019774 [1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...]
= [1;1,(1,1,4p+1)], p∈ℕ
i Numero imaginario {i} \sqrt{-1} = \frac{\ln(-1)}{\pi} \qquad\qquad \mathrm{e}^{i\,\pi} = -1 sqrt(-1) C
262537412640768743,999999999999250073 Constante de Hermite-Ramanujan {R}  e^{\pi\sqrt{163}} e^(π sqrt(163)) T A060295 [262537412640768743;1,1333462407511,1,8,1,1,5,...]
4,81047738096535165547303566670383313 Constante de John  \gamma \sqrt[i]{i} = i^{-i} = i^{\frac{1}{i}} = (i^i)^{-1} = e^{\frac{\pi}{2}} e^(π/2) T A042972 [4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,...]
4,53236014182719380962768294571666681 Constante de Van der Pauw  \alpha \frac{\pi}{ln(2)} = \frac{\sum_{n = 0}^\infty \frac{4(-1)^n}{2n+1}} {\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}} = \frac{\frac{4}{1} {-} \frac{4}{3} {+} \frac{4}{5} {-} \frac{4}{7} {+} \frac{4}{9} - ...} {\frac{1}{1}{-}\frac{1}{2}{+}\frac{1}{3}{-}\frac{1}{4}{+}\frac{1}{5}-...} π/ln(2) T A163973 [4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...]
0,76159415595576488811945828260479359 Tangente hiperbólica de 1 th \, 1 \frac{e-\frac{1}{e}}{e+\frac{1}{e}} = \frac{e^2-1}{e^2+1} (e-1/e)/(e+1/e) T A073744 [0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...]
= [0;(2p+1)], p∈ℕ
0,69777465796400798200679059255175260 Constante de fraccion continua {C}_{CF}  \underset{J_{k}() {Bessel}}\underset{{Funci\acute{o}n}}\frac{J_1(2)}{J_0(2)} = \frac{ \sum\limits_{n = 0}^{\infty} \frac{n}{n!n!}} {{ \sum\limits_{n = 0}^{\infty} \frac{1}{n!n!}}} = \frac{\frac{0}{1}+\frac{1}{1}+\frac{2}{4}+\frac{3}{36}+\frac{4}{576}+...} {\frac{1}{1}+\frac{1}{1}+\frac{1}{4}+\frac{1}{36}+\frac{1}{576}+...} (sum {n=0 to inf} n/(n!n!)) /(sum {n=0 to inf} 1/(n!n!)) A052119 [0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...]
= [0;(p+1)], p∈ℕ
0,36787944117144232159552377016146086 Inverso del Numero neperian 1/e \sum_{n = 0}^\infty \frac{(-1)^n}{n!} = \frac{1}{0!} - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} +\cdots sum[n=2 to ∞]{(-1)^n/n!} T A068985 [0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...]
= [0;2,1,(1,2p,1)], p∈ℕ
2,71828182845904523536028747135266250 Numero neperian, constante de Euler e \sum_{n = 0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \cdots Sum[n=0 to ∞]{1/n!} T A001113 [2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...]
= [2;(1,2p,1)], p∈ℕ
0,49801566811835604271369111746219809
- 0,15494982830181068512495513048388 i
Factorial de i i !  \Gamma (1+i) = i \Gamma (i) Gamma(1+i) A212877
A212878
[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...]
- [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i
0,43828293672703211162697516355126482
+ 0,36059247187138548595294052690600 i
Tetración infinite de i   {}^\infty i   \lim_{n \to \infty}  {}^n i  =  \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n  i^i^i^... A077589
A077590
[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...]
+ [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i
0,56755516330695782538461314419245334 Modulo de la
Tetración infinite de i
 | {}^\infty i |  \lim_{n \to \infty} \left | {}^n i \right |  =\left | \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n  \right | Mod(i^i^i^...) A212479 [0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...]
0,26149721284764278375542683860869585 Constante de Meissel-Mertens M \lim_{n \rightarrow \infty } \left( 
\sum_{p \leq n} \frac{1}{p}  - \ln(\ln(n)) \right) ..... p: primos A077761 [0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]
1,9287800... Constante de Wright ω \left \lfloor 2^{2^{2^{\cdot^{\cdot^{2^{\omega}}}}}} \right \rfloor = primos: \quad \left\lfloor 2^\omega\right\rfloor =3, \left\lfloor 2^{2^\omega} \right\rfloor =13, \left\lfloor 2^{2^{2^\omega}} \right\rfloor =16381, \dots A086238 [1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
0,37395581361920228805472805434641641 Constante de Artin CArtin \prod_{n=1}^{\infty} \left(1-\frac{1}{p_n(p_n-1)}\right) ...... pn: primo T A005596 [0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]
4,66920160910299067185320382046620161 Constante δ de Feigenbaum δ  \lim_{n \to \infty}\frac {x_{n+1}-x_n}{x_{n+2}-x_{n+1}} ......  x \in (3,8284; 3,8495)

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

T A006890 [4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
2,50290787509589282228390287321821578 Constante α de Feigenbaum α \lim_{n \to \infty}\frac {d_n}{d_{n+1}} T A006891 [2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
5,97798681217834912266905331933922774 Constante hexagonal Madelung 2 H2(2)  \pi \ln(3) \sqrt 3 Pi Log[3]Sqrt[3] T A086055 [5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]
0,83462684167407318628142973279904680 Constante de Gauss GGa  \frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{[\Gamma(\tfrac14)]^2}{(2 \pi)^{3/2}} Γ[1/4]]^2/(2*Pi^{3/2}*Sqrt(2) T A014549 [0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]
0,96894614625936938048363484584691860 Constante Beta(3) β(3)  \frac{\pi^3}{32} = \sum_{n=1}^\infty\frac{-1^{n+1}}{(-1+2n)^3} = \frac{1}{1^3}-\frac{1}{3^3} + \frac{1}{5^3} - \frac{1}{7^3} + \cdots\,\! Sum[n=1 to ∞]{(-1)^(n+1)/(-1+2n)^3} T A153071 [0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...]
1,902160583104 Constante de Brun 2 = Σ inv. numeros primos gemelos B 2  \textstyle \sum (\frac1{p}+\frac1{p+2}) = (\frac1{3} + \frac1{5}) + (\tfrac1{5} + \tfrac1{7}) + (\tfrac1{11} + \tfrac1{13}) + \ldots

p, p+2 primos

A065421 [1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
0,870588379975 Constante de Brun 4 = Σ inv. numeros primos gemelos B 4  \left(\tfrac1{5} + \tfrac1{7} + \tfrac1{11} + \tfrac1{13}\right)
+ \left(\tfrac1{11} + \tfrac1{13} + \tfrac1{17} + \tfrac1{19}\right)+ \ldots

p, p+2, p+4, p+6 primos

A213007 [0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22,4591577183610454734271522045437350 pi^e πe \pi^{e} pi^e A059850 [22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]
3,14159265358979323846264338327950288 Numero π, constante de Arquimedes π \lim_{n\to \infty }\, 2^{n} \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\text{...} +\sqrt{2}}}}}_n Sum[n=0 to ∞]{(-1)^n 4/(2n+1)} T A000796 [3;7,15,1,292,1,1,1,2,1,3,1,14,...]
0,06598803584531253707679018759684642 e-e e^{-e} ... Limite inferior de Tetración T A073230 [0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...]
0,20787957635076190854695561983497877 i^i ii  e^ \frac{-\pi}{2} e^(-pi/2) T A049006 [0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...]
0,28016949902386913303643649123067200 Constante de Bernstein β \frac {1}{2\sqrt {\pi}} T A073001 [0;3,1,1,3,9,6,3,1,3,13,1,16,3,3,4,…]
0,28878809508660242127889972192923078 Flajolet and Richmond Q  \prod_{n=1}^{\infty} \left(1 - \frac{1}{2^n}\right) = \left(1-\frac{1}{2^1}\right) \left(1-\frac{1}{2^2} \right)\left(1-\frac{1}{2^3} \right)\cdots prod[n=1 to ∞]{1-1/2^n} A048651
0,31830988618379067153776752674502872 Inverso de Pi, Ramanujan 1/π  \frac{2\sqrt{2}}{9801} \sum^\infty_{n=0} \frac{(4n)!(1103+26390n)}{(n!)^4 396^{4n}} T A049541 [0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...]
0,47494937998792065033250463632798297 Constante de Weierstrass WWE  \frac{e^{\frac{\pi}{8}}\sqrt{\pi}}{4*2^{3/4} {(\frac {1}{4}!)^2}} (E^(Pi/8) Sqrt[Pi])/(4 2^(3/4) (1/4)!^2) T A094692 [0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,...]
0,56714329040978387299996866221035555 Constante Omega Ω=W(1) \sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!} = 1 - 1 + \frac{3}{2} - \frac{8}{3} + \frac{125}{24} - \cdots sum[n=1 to ∞]{(-n)^(n-1)/n!} T A030178 [0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,...]
0,57721566490153286060651209008240243 Constante de Euler-Mascheroni γ  -\psi(1) = \sum_{n=1}^\infty \sum_{k=0}^\infty \frac{(-1)^k}{2^n+k} sum[n=1 to ∞]|sum[k=0 to ∞]{((-1)^k)/(2^n+k)} ? A001620 [0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,...]
0,60459978807807261686469275254738524 Serie de Dirichlet π/(3√3)  \frac{\pi}{3 \sqrt 3} = \sum_{n = 1}^\infty \frac{1}{n{2n \choose n}} =  1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{5} + \frac{1}{7} - \frac{1}{8} + \cdots Sum[1/(n Binomial[2 n, n]), {n, 1, ∞}] T A073010 [0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,...]
0,63661977236758134307553505349005745 2/Pi por, François Viète 2/π  \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots T A060294 [0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
0,66016181584686957392781211001455577 Constante de los primos gemelos C2 \prod_{p=3}^\infty \frac{p(p-2)}{(p-1)^2} prod[p=3 to ∞]{p(p-2)/(p-1)^2 A005597 [0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...]
0,66274341934918158097474209710925290 Constante límite de Laplace λ A033259 [0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0,69314718055994530941723212145817657 Logaritmo natural de 2 Ln(2) \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} = \frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\cdots Sum[n=1 to ∞]{(-1)^(n+1)/n} T A002162 [0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...]
0,78343051071213440705926438652697546 Sophomore's Dream 1 J.Bernoulli I1 \sum_{n = 1}^\infty \frac{(-1)^{n+1}}{n^n} = 1 - \frac{1}{2^2} + \frac{1}{3^3} - \frac{1}{4^4} + \frac{1}{5^5} - \frac{1}{6^6}+ \cdots Sum[ -(-1)^n /n^n] T A083648 [0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,...]
0,78539816339744830961566084581987572 Dirichlet beta β(1) π/4 \sum_{n = 0}^\infty \frac{(-1)^n}{2n+1} = \frac{1}{1} - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \cdots Sum[n=0 to ∞]{(-1)^n/(2n+1)} T A003881 [0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,...]
0,82246703342411321823620758332301259 Traveling Salesman, Nielsen-Ramanujan ζ(2)/2  \frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} - \frac{1}{2^2} + \frac{1}{3^2} - \frac{1}{4^2} + \frac{1}{5^2} -\cdots Sum[n=1 to ∞]{((-1)^(k+1))/n^2} T A072691 [0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,...]
0,91596559417721901505460351493238411 Constante de Catalan C \sum_{n = 0}^\infty \frac{(-1)^n}{(2n+1)^2} = \frac{1}{1^2}-\frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\cdots Sum[n=0 to ∞]{(-1)^n/(2n+1)^2} I A006752 [0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1,05946309435929526456182529494634170 Constante entre semitonos de la escala musical 12√2 \sqrt[12]{2} 2^(1/12) I A010774 [1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]
1,08232323371113819151600369654116790 Constante Zeta(04) ζ(4)  \frac{\pi^4}{90} = \sum_{n=1}^\infty\frac{{1}}{n^4} = \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \frac{1}{4^4} + \frac{1}{5^4} + \frac{1}{6^4} +\cdots Sum[n=1 to ∞]{1/n^4} T A013662 [1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,...]
1,1319882487943 ... Constante de Viswanath CVi \lim_{n \to \infty}|a_n|^\frac{1}{n} A078416 [1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]
1,20205690315959428539973816151144999 Constante de Apery ζ(3) \sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots\,\! Sum[n=1 to ∞]{1/n^3} I A010774 [1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,...]
1,22541670246517764512909830336289053 Gamma(3/4) Γ(¾) \left(-1+\frac{3}{4}\right)! (-1+3/4)! T A068465 [1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,...]
1,23370055013616982735431137498451889 Constante de Favard ¾ ζ(2)  \frac{\pi^2}{8} = \sum_{n = 0}^\infty \frac{1}{(2n-1)^2} = \frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots sum[n=1 to ∞]{1/((2n-1)^2)} T A111003 [1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...]
1,25992104989487316476721060727822835 Radice cubica de dos, constante Delian 3√2 \sqrt[3]{2} 2^(1/3) I A002580 [1;3,1,5,1,1,4,1,1,8,1,14,1,10,...]
1,29128599706266354040728259059560054 Sophomore's Dream 2 J.Bernoulli I2  \sum_{n = 1}^\infty \frac{1}{n^n} =  1 + \frac{1}{2^2} + \frac{1}{3^3} + \frac{1}{4^4} + \frac{1}{5^5} + \frac{1}{6^6} + \frac{1}{7^7} + \cdots Sum[1/(n^n]), {n, 1, ∞}] A073009 [1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,...]
1,32471795724474602596090885447809734 Numero plástico ρ \sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \sqrt[3]{1 + \cdots}}}} I A060006 [1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...]
1,41421356237309504880168872420969808 Radice cuadrada de 2, constante de Pitagoras √2 \prod_{n=1}^\infty 1+\frac{(-1)^{n+1}}{2n-1} = \left(1+\frac{1}{1}\right) \left(1-\frac{1}{3} \right)\left(1+\frac{1}{5} \right)\cdots prod[n=1 to ∞]{1+(-1)^(n+1)/(2n-1)} I A002193 [1;(2),...]
1,44466786100976613365833910859643022 Numero de Steiner e1/e e^{1/e} ... Límite superior de Tetración A073229 [1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
1,53960071783900203869106341467188655 Constante Square Ice de Lieb W2D \lim_{n \to \infty}(f(n))^{n^{-2}}=\left(\frac{4}{3}\right)^\frac{3}{2} (4/3)^(3/2) I A118273 [1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...]
1,57079632679489661923132169163975144 Producto de Wallis π/2  \prod_{n=1}^{\infty} (\frac{4n^2}{4n^2 - 1}) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots 
T A019669 [1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1...]
1,60669515241529176378330152319092458 Constante de Erdős–Borwein EB \sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} + \frac{1}{3} + \frac{1}{7} + \frac{1}{15} + \cdots\,\! sum[n=1 to ∞]{1/(2^n-1)} I A065442 [1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...]
1,61803398874989484820458633436563812 Fi, Número áureo Φ \frac{1 + \sqrt{5}}{2} = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}} (1+5^(1/2))/2 I A001622 [0;(1),...]
1,64493406684822643647241516664602519 Función Zeta (2) de Riemann ζ(2)  \frac{\pi^2}{6} = \sum_{n=1}^\infty\frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots Sum[n=1 to ∞]{1/n^2} T A013661 [1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...]
1,66168794963359412129581892274995074 Recurrencia cuadrática de Somos σ \sqrt {1 \sqrt {2 \sqrt{3 \cdots}}} = 1^{1/2} ; 2^{1/4} ; 3^{1/8} \cdots T A065481 [1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
1,73205080756887729352744634150587237 Constante de Theodorus √3 \sqrt{3} 3^(1/2) I A002194 [1;(1,2),...]
1,75793275661800453270881963821813852 Numero de Kasner K \sqrt{1 + \sqrt{2 + \sqrt{3 + \sqrt{4 + \cdots}}}} A072449 [1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
1,77245385090551602729816748334114518 Constante de Carlson-Levin Γ(1/2) \sqrt{\pi} = \left(-\frac{1}{2}\right)! sqrt (pi) T A002161 [1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]
2,23606797749978969640917366873127624 Radice quadrate de 5 √5 \sqrt{5} 5^(1/2) I A002163 [2;(4),...]
2,29558714939263807403429804918949038 Constante universal parabolic P2 \ln(1 + \sqrt2) + \sqrt2 ln(1+sqrt 2)+sqrt 2 T A103710 [2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,...]
2,30277563773199464655961063373524797 Numero de bronce σBr \frac {3+\sqrt{13}}{2} = 1+ \sqrt{3+\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}} (3+sqrt 13)/2 I A098316 [3;(3),...]
2,37313822083125090564344595189447424 Constante de Levy 2 2lnγ \frac{\pi^2}{6ln(2)} Pi^(2)/(6*ln(2)) T A174606 [2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]
2,50662827463100050241576528481104525 Radice quadrate de 2 pi (2π)1/2 \sqrt{2 \pi} sqrt (2*pi) T A019727 [2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]
2,66514414269022518865029724987313985 Constante de Gelfond-Schneider GGS 2^{\sqrt{2}} 2^sqrt{2} T A007507 [2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...]
2,68545200106530644530971483548179569 Constante de Khintchin K0  \prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\ln n/\ln 2} prod[n=1 to ∞]{(1+1/(n(n+2)))^((ln(n)/ln(2))} ? A002210 [2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...]
3,27582291872181115978768188245384386 Constante de Khinchin-Lévy γ  e^{\pi^2/(12\ln2)} e^(\pi^2/(12 ln(2)) A086702 [3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...]
3,35988566624317755317201130291892717 Constante de los inversos de Fibonacci ψ \sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} +  \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots A079586 [3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4,13273135412249293846939188429985264 Raíz de 2 e pi √(2eπ)  \sqrt{2e \pi} sqrt(2e pi) T A019633 [4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]
6,58088599101792097085154240388648649 Constante de Froda 2e 2^e  2^e [6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...]
9,86960440108935861883449099987615114 Pi al Cuadrado π2 6 \sum_{n=1}^\infty \frac{1}{n^2} = \frac{6}{1^2} + \frac{6}{2^2} + \frac{6}{3^2} + \frac{6}{4^2}+ \cdots 6 Sum[n=1 to ∞]{1/n^2} T A002388 [9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,...]
23,1406926327792690057290863679485474 Constante de Gelfond eπ \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2!} + \frac{\pi^{3}}{3!} + \frac{\pi^{4}}{4!}+ \cdots Sum[n=0 to ∞]{(pi^n)/n!} T A039661 [23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]

references[modificar | modificar fonte]

Ligamines externe[modificar | modificar fonte]

Creditos y recognocimientos[modificar | modificar fonte]

Correction de formulas: M.Romero Schmidtke

Colaborations[modificar | modificar fonte]

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