Costante matematica

Nome

Simbolo

Valore

Significato

Pi greco, costante di Archimede o numero di Ludoph

π

≈3.141592653589793

Un numero trascendentale che è il rapporto tra la lunghezza della circonferenza di un cerchio e il suo diametro. È anche l'area del cerchio unitario.

E, costante di Napier

e

≈2.718281828459045

Un numero trascendentale che è la base dei logaritmi naturali, talvolta chiamato "numero naturale".

Rapporto aureo

φ

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

È il valore di un valore maggiore diviso per un valore minore se questo è uguale al valore della somma dei valori diviso per il valore maggiore.

Radice quadrata di 2, costante di Pitagora

2 {displaystyle {sqrt {2}}

1.414

Un numero irrazionale che è la lunghezza della diagonale di un quadrato con lati di lunghezza 1. Questo numero non può essere scritto come frazione.

Valore

Nome

Simbolo

LaTeX

Formula

Tipo

OEIS

Frazione continua

3.24697960371746706105000976800847962

Argento, costante Tutte-Beraha

{\an8}(*Città che si trova al centro della città.)

2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 7 + 7 7 + 7 + 7 + ⋯ 3 3 3 1 + 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

Parigi costante

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

Ramanujan annidato radicale R5

R 5 {displaystyle R_{5}

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 }}}}}}}}}}}}}}\;==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

Radice quadrata di 5, somma di 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 \\=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}}=1+e^{\frac {2\pi i}{5}+e^{\frac {8\pi i}{5}+e^{\frac {18\pi i}{5}}}

Somma[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 ) ! {\fscala 4\frac {1}{4}} a destra!=\frac {3}{4} a destra)= a sinistra(-{frac {3}{4}} a destra)! }

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

Costante MRB, 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 \sum _{n=1}^{infty }({-}1)^{n}(n^{1/n}{-}1)=-{sqrt[1}]{1}+{sqrt[2}]{2}-{sqrt[3}]{3}+{sqrt[4}]{4}},\punti}

Somma[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

Costante di Keplero-Bouwkamp

ρ {displaystyle {rho}

∏ n = 3 ∞ cos ( π n ) = cos ( π 3 ) cos ( π 4 ) cos ( π 5 ) ... {displaystyle \prod _{n=3}^{infty }cos \left({\frac 3)=cos \sinistra(4)=cos \sinistra(4)=cos \sinistra(5)=destra)=cos \sinistra(4)=destra)=cos \sinistra(5)=punti

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

Exp(gamma)
Funzione 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 ¡scegliere k}}{right)^{\frac {1}{n+1}}=}

( 2 1 ) 1 / 2 ( 2 2 1 ⋅ 3 ) 1 / 3 ( 2 3 ⋅ 4 1 ⋅ 3 3 ) 1 / 4 ( 2 4 ⋅ 4 4 1 ⋅ 3 6 ⋅ 5 ) 1 / 5 ... {\displaystyle \textstyle \left({\frac {2}{1}}}right)^{1/2} {\frac 3) a destra)1/3) a sinistra(2) a sinistra(2) a destra(3) a destra)1/4) a sinistra(2) a destra(4) a sinistra(1) a destra)1/5) a sinistra(2) a destra(4) a destra(1) a destra(6) a destra)

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

Costante di 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)}=e^{{frac {1}{8}-{frac {1}{2}} somma \limiti _{n=0}^{infty }{frac {1}{n+1}}} somma \limiti _{k=0}^{n} a sinistra (-1) a destra)^{k}{binom {n}{k}} a sinistra (k+1) a destra)^{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

Costante conica di 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 \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!}+punti }

Somma[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, ecc.

1.01494160640965362502120255427452028

Costante di 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{sqrt {3}}}{4}} a sinistra(1-somma _{n=0}^{infty }{frac {1}{(3n+2)^{2}}}+somma _{n=1}^{infty }{frac {1}{(3n+1)^{2}}} diritto)=}

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}} a sinistra(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 \punti \destra)} .

T

A143298

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

2.62205755429211981046483958989111941

Lemniscata costante

ϖ {displaystyle {varpi}

π G = 4 2 π ( 1 4 ! ) 2 {displaystyle \pi \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

Costante di 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 o {\displaystyle {\underset {Agm:\;Aritmetico-geometrico\;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 ) {\displaystyle \zeta (6)}

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 }{underset {p_{n}:\,{primo}}}{frac {1}{1}-p_{n}^{-6}}}}={frac {1}{1{1{-}2^{-6}}{\frac {1}{1{1{-}3^{-6}}{\frac {1}{1}{1{1{-}5^{-6}}}... }

Prod[n=1 a ∞] {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

Costante di 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 }{underset {p_{n}:{\an8}{primo}}{{{1}frac {1}{{p_{n}}^{2}}}destra)}}{{textstyle \left(1{-}{{frac {1}{2^{2}}}destra)\left(1{-}{frac {1}{3^{2}}}destra)\left(1{-}{frac {1}{5^{2}}}destra)\punti }

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

Il rapporto tra un quadrato e i cerchi circoscritti o inscritti

π 2 2 2 {displaystyle {frac {pipi}{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 \sum _{n=1}^{\infty }(-1)^{{lfloor {\frac {n-1}{2}{2n+1}}}={frac {1}{1}}+{frac {1}{3}-{frac {1}{5}-{frac {1}{7}+{frac {1}{9}+{frac {1}{11}}- punti}

sum[n=1 a ∞]{(-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

Costante di 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}}{\frac {e^{{\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

Radice quadrata del numero 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 \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{48}}}

somma[n=0 a ∞]{1/(2^n n!)}

T

A019774

[1;1,1,1,1,5,1,1,9,1,1,1,13,1,1,17,1,1,21,1,1,...]
= [1;1,(1,1,4p+1)], p∈ℕ

i

Numero immaginario

i {displaystyle {i}

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

sqrt(-1)

C

262537412640768743.999999999999250073

Costante di Hermite-Ramanujan

R {displaystyle {R}

e π 163 {displaystyle e^{{pi {163}}}}

e^(π sqrt(163))

T

A060295

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

4.81047738096535165547303566670383313

Giovanni costante

γ γ γ γ γ γ γ γ γ γ γ

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

Costante de Van der Pauw

αdisplaystyle \alpha }

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

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 iperbolica (1)

t h 1 {displaystyle 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

Costante di frazione continua

C C F {C} {C}_{CF}

J 1 ( 2 ) J 0 ( 2 ) F u n z i o n e J k ( ) B e s 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 {\underset {J_{k}(){Bessel}}{underset {Funzione}{frac {J_{1}(2)}{J_{0}(2)}}}}={frac {sum \limits _{n=0}^{\infty}{\frac {n}{n!n!={sum \limiti _{n=0}^{infty}^{frac {1}{n!n!}}}}={{frac {0}{1}}+{frac {1}{1}}+{frac {2}{4}}+{frac {3}{36}}+{frac {4}{576}}+puntini }{frac {1}{1}}+{frac {1}{1}{1}+{frac {1}{4}}+{frac {1}{36}}+{frac {1}{576}}}

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

Costante di Napier inversa

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

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

somma[n=2 a ∞]{(-1)^n/n!}

T

A068985

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

2.71828182845904523536028747135266250

Costante di Napier

e {displaystyle e}

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

Somma[n=0 a ∞]{1/n!}

T

A001113

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

0.49801566811835604271369111746219809
- 0.15494982830181068512495513048388 i

Fattoriale di i

i ! i ! }

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
Tetrazione di i

∞ i {displaystyle {}^{infty }i}

lim n → ∞ n i = lim n → ∞ i i ⋅ ⋅ i ⏟ n {\displaystyle \lim _{n\a6}^{n}i=lim _{n\a6} a \a6} i=lim _{n\a6} a \a6} sottobraccio {i^{i^{{{\a6}cdot ^{\a6}}}}}} _{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

Modulo di
infinito
Tetrazione di i

{\an8}(*Circostanza)

lim n → ∞ | n i | = | lim n → ∞ i i ⋅ ⋅ i ⏟ n | {\displaystyle \lim _{n{ a sinistra ∞ i ⏟ n | {\displaystyle \lim _{ a sinistra ∞ i ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ i {\an8}destra}

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

Costante di Meissel-Mertens

M {displaystyle M}

lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) {\displaystyle \lim _{n\code(01)\destra \infty}(\somma _{p\leq n}{frac {1}{p}}- \ln(\ln(n))\destra)} ..... p: primati

A077761

[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]

1.9287800...

Costante di Wright

ω \displaystyle \omega }

⌊ 2 2 2 ⋅ ⋅ 2 ω ⌋ {displaystyle 【left\lfloor 2^{2^{2^{2^{cdot ^{cdot ^{2^{omega }}}}}}\right\rfloor } = primos: ‗displaystyle', ‗quadro'.  ⌊ 2 2 2 ω ⌋ {displaystyle ）left\lfloor 2^{2^{2^{omega}}}destra\rfloor } =16381, ... {displaystyle ）punti}

A086238

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

0.37395581361920228805472805434641641

Artin costante

C A r t i n {displaystyle C_Artin}

∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \prod _{n=1}^{\infty}left(1-{frac {1}{p_{n}(p_{n}-1)}}right)} ...... 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

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

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

T

A006890

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

2.50290787509589282228390287321821578

Costante di Feigenbaum α

αdisplaystyle \alpha }

lim n → ∞ d n d n + 1 {displaystyle \lim _{n\a6} a \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

Madelung esagonale costante ₂

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

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

Pi Log[3]Sqrt[3]

T

A086055

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

0.96894614625936938048363484584691860

Beta(3)

β ( 3 ) {\displaystyle \beta (3)}

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

Somma[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

Brun costante ₂ = Σ primati gemelli inversi

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,\,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})+\punti}

A065421

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

0.870588379975

Brun costante ₄ = Σ inverso del primo gemello

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,p,p+4,\6:\primi}}}{sinistra(\tfrac {1}{5}+{tfrac {1}{7}}+{tfrac {1}{11}}+{tfrac {1}{13}}destra)}}+sinistra(\tfrac {1}{11}+{tfrac {1}{13}}+{tfrac {1}{17}}+{tfrac {1}{19}}destra)+\punti }

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 greco, costante di Archimede

π \displaystyle \più

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

Somma[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}} ... Limite inferiore della tetrazione

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 {\displaystyle 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

Costante di Bernstein

β {displaystyle \beta }

1 2 π {displaystyle {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 e Richmond

Q {displaystyle Q}

∏ n = 1 ∞ ( 1 - 1 2 n ) = ( 1 - 1 2 1 ) ( 1 - 1 2 2 ) ( 1 - 1 2 3 ) ... {\displaystyle \prod _{n=1}^{\infty}left(1-{\frac {1}{2^{n}}}}destra)==sinistra(1{-}{frac {1}{2^{1}}}destra)\sinistra(1{-}{frac {1}{2^{2}}}destra)\sinistra(1{-}{frac {1}{2^{3}}}destra)\punti }

prod[n=1 a ∞]{1-1/2^n}

A048651

0.31830988618379067153776752674502872

Inverso di 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{\sqrt {2}}{9801}}}{sum _{n=0}^{infty }{frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}}

T

A049541

[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,...]

0.47494937998792065033250463632798297

Costante Weierstraß

W W E {\displaystyle W_{_{WE}}}

e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {displaystyle {e^{{frac {\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

Costante Omega

Ω {displaystyle \mega }

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

sum[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

Numero di Eulero

γ γ γ γ γ γ γ γ γ γ γ

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

somma[n=1 a ∞]|somma[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 di Dirichlet

π 3 3 3 {displaystyle {frac {pipi}{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}{n{2n \scegliere n}}}=1-1... 1... 2... + 1... 4... 4... 4... 5... + 1... 7... 7... 8... 8...

Somma[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}{\i}

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

T

A060294

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

0.66016181584686957392781211001455577

Costante primaria gemella

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

Costante del limite di Laplace

λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ

A033259

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

0.69314718055994530941723212145817657

Logaritmo di 2

L n ( 2 ) {\displaystyle 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}}{1}}-{frac {1}{2}}+{frac {1}{3}}-{frac {1}{4}+{frac {1}{5}}-\cdots }

Somma[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

Il sogno del secondo anno ₁ J.Bernoulli

I 1 {displaystyle I_{1}}

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

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

T

A083648

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

0.78539816339744830961566084581987572

Dirichlet beta(1)

β ( 1 ) {\displaystyle \beta (1)}

π 4 = ∑ n = 0 ∞ ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - ⋯ {\displaystyle {\frac {\frac {\pi }4}}=somma _{n=0}^{infty }{\frac {(-1)^{n}}{2n+1}}={frac {1}{1}}-{frac {1}{3}}+{frac {1}{5}}-{frac {1}{7}}+{frac {1}{9}}-\code(01)}

Somma[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

Commesso viaggiatore Nielsen-Ramanujan

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

π 2 12 = ∑ n = 1 ∞ ( - 1 ) n + 1 n 2 = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 - ... {\displaystyle {\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}}- punti }

Somma[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

Costante catalana

C {displaystyle 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 }

Somma[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

Rapporto della distanza tra i semitoni

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 {displaystyle \zeta {4}

π 4 90 = ∑ n = 1 ∞ 1 n 4 = 1 1 4 + 1 2 4 + 1 3 4 + 1 4 4 + 1 5 4 + ... {\displaystyle {\frac {{pi ^{4}{90}}=somma _{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}}+punti }

Somma[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 costante

C V i {displaystyle C_{Vi}

lim n → ∞ | a n | 1 n {displaystyle \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

Costante di apetito

ζ ( 3 ) {\displaystyle \zeta (3)}

∑ 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 }^{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}}+capitoli \, }

Somma[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 ) ! { {\frac {\frac {3}{4}} a destra) ! }

(-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

Costante di Favard

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

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

somma[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

Radice al cubo di 2, costante 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

Il sogno del secondo anno ₂ J.Bernoulli

I 2 {displaystyle I_{2}

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

Somma[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 di plastica

ρ {displaystyle \rho }

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

I

A060006

[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,...]

1.41421356237309504880168872420969808

Radice quadrata di 2, costante di Pitagora

2 {displaystyle {sqrt {2}}

∏ n = 1 ∞ 1 + ( - 1 ) n + 1 2 n - 1 = ( 1 + 1 1 ) ( 1 - 1 3 ) ( 1 + 1 5 ) . . . {\displaystyle \prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}==sinistra(1{+}{\frac {1}{1}}}destra)\sinistra(1{-}{\frac {1}{3}}destra)\sinistra(1{+}{\frac {1}{5}}destra)... }

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

Numero di Steiner

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

e 1 / e {\displaystyle e^{1/e}} ... Limite superiore della tetrazione

A073229

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

1.53960071783900203869106341467188655

Lieb's Square Ice costante

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

lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 {displaystyle \lim _{n{ a \infty }(f(n))^{n^{-2}}={ a sinistra({\frac {4}{3}} a destra)^{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

Prodotto Wallis

π / 2 {displaystyle \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}-1}destra)={frac {2}{1}}}cdot {2}{3}}{frac {4}{3}}{frac {4}{5}}{frac {6}{5}}{frac {6}{7}}{frac {8}{7}{8}{9}}

T

A019669

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

1.60669515241529176378330152319092458

costante di Erdős-Borwein

E B {\anime E_{\anime,B}}

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

somma[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, rapporto aureo

φ {displaystyle \varphi }

1 + 5 2 = 1 + 1 + 1 + 1 + 1 + ⋯ {displaystyle {frac {1+{sqrt {5}}{2}={sqrt {1+{sqrt {1+{sqrt {1+{sqrt {1+{punti }}}}}}}}}

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

I

A001622

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

1.64493406684822643647241516664602519

Zeta(2)

ζ ( 2 ) {\displaystyle \zeta (\2)}

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}=somma _{n=1}}^{infty }{frac {1}{n^{2}}={frac {1}{1^{2}}+{frac {1}{2^{2}}}+{frac {1}{3^{2}}+{frac {1}{4^{2}}+{cdots }

Somma[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

Costante di ricorrenza quadratica di Somos

σ \displaystyle \sigma }

1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {\displaystyle {\sqrt {1{sqrt {2{sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots }

T

A065481

[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]

1.73205080756887729352744634150587237

Costante di 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

Numero Kasner

R {displaystyle R}

1 + 2 + 3 + 4 + ⋯ {displaystyle {sqrt {1+{sqrt {2+{sqrt {3+{sqrt {4+capitoli }}}}}}}}}

A072449

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

1.77245385090551602729816748334114518

Costante Carlson-Levin

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

π = ( − 1 2 ) ! {displaystyle {sqrt {\i}=sinistra(-{frac {1}{2}}destra) !) }

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

Costante parabolica universale

P 2 {displaystyle P_{\2}

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

ln(1+sqrt 2)+sqrt 2

T

A103710

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

2.30277563773199464655961063373524797

Numero di bronzo

σ R r {\displaystyle \sigma _{{ Rr}}

3 + 13 2 = 1 + 3 + 3 + 3 + 3 + 3 + ⋯ {displaystyle {frac {3+{sqrt {13}}{2}}=1+{sqrt {3+{sqrt {3+{sqrt {3+{sqrt {3+{sqrt }}}}}}}}}

(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

Costante di Lévy2

2 ln γ {displaystyle 2,\ln \gamma }

π 2 6 ln ( 2 ) {displaystyle {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

radice quadrata di 2 pi greco

2 π {displaystyle {sqrt {2\pi}

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

sqrt (2*pi)

T

A019727

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

2.66514414269022518865029724987313985

Costante di Gelfond-Schneider

2 2 2 {displaystyle 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

Costante di 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 \sopra n(n+2)}destra]^{\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

Costante di Khinchin-Lévy

γ γ γ γ γ γ γ γ γ γ γ

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

Costante di Fibonacci reciproca

Ψ {displaystyle \Psi }

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

A079586

[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]

4.13273135412249293846939188429985264

Radice di 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

Costante di Froda

2 e {displaystyle 2^{\a6}

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 quadrato

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\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 Somma[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

Costante Gelfond

e π {displaystyle e^{\i}

∑ n = 0 ∞ π n n ! = π 1 1 + π 2 2 ! + π 3 3 ! + π 4 4 ! + ⋯ {displaystyle \sum _{n=0}^{infty }{frac {\pi ^{n}}{n!}={frac {\pi ^{1}}{1}+{frac {\pi ^{2}}{2!}+{frac {\pi ^{3}{3!}+{frac {\pi ^{4}{4!}+cdots }

Somma[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,...]