Costante matematica

Una costante matematica è un numero che ha un significato speciale per i calcoli. Per esempio, la costante π (pronunciato "pie") significa il rapporto tra la circonferenza di un cerchio e il suo diametro. Questo valore è sempre lo stesso per qualsiasi cerchio. Una costante matematica è spesso un numero reale non integrale di interesse.

A differenza delle costanti fisiche, le costanti matematiche non provengono da misure fisiche.

Costanti matematiche chiave

La seguente tabella contiene alcune importanti costanti matematiche:

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} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	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}} ${\sqrt {2}}$	1.414 $\approx 1.414$	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.

Costanti e serie

La seguente tabella contiene un elenco di costanti e serie in matematica, con le seguenti colonne:

Valore: Valore numerico della costante.
LaTeX: Formula o serie in formato TeX.
Formula: Per l'uso in programmi come Mathematica o Wolfram Alpha.
OEIS: Link alla On-Line Encyclopedia of Integer Sequences (OEIS), dove le costanti sono disponibili con maggiori dettagli.
Frazione continua: Nella forma semplice [a intero; frac1, frac2, frac3, ...] (tra parentesi se periodica)
Tipo:

R - Numero razionale
I - Numero irrazionale
T - Numero trascendentale
C - Numero complesso

Nota che la lista può essere ordinata in modo corrispondente cliccando sul titolo dell'intestazione in cima alla tabella.

Valore	Nome	Simbolo	LaTeX	Formula	Tipo	OEIS	Frazione continua
3.24697960371746706105000976800847962	Argento, costante Tutte-Beraha	{\an8}(*Città che si trova al centro della città.) $\varsigma$	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 }}}}}}}}} $2+2\cos(2\pi /7)=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}$	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}} $C_{Pa}$	∏ n = 2 ∞ 2 φ φ + φ n , φ = F i {\displaystyle \prod _{n=2}^{\infty }{frac {2\varphi }{varphi +\varphi _{n}}};,\varphi ={Fi}} $\prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\varphi ={Fi}$		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} $R_{5}$	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}} $\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(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	Radice quadrata di 5, somma di Gauss	5 {displaystyle {sqrt {5}} ${\sqrt {5}}$	∀ 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}}} $\scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	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}})} $\Gamma ({\tfrac {1}{4}})$	4 ( 1 4 ) ! = ( − 3 4 ) ! {\fscala 4\frac {1}{4}} a destra!=\frac {3}{4} a destra)= a sinistra(-{frac {3}{4}} a destra)! } $4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	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	Costante MRB, Marvin Ray Burns	C M R B {\displaystyle C_{_{MRB}}} $C_{_{MRB}}$	∑ 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} $\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots$	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} ${\rho }$	∏ 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 $\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)\dots$	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} $e^{\gamma }$	∏ 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}}=} $\prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}=$ ( 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) $\textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/5}\dots$	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} ${A}$	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)}} $e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	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	Costante conica di Schwarzschild	e 2 {displaystyle e^{2}} $e^{2}$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots$	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}} ${G_{Gi}}$	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)=} ${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ 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)} $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)$ .		T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2.62205755429211981046483958989111941	Lemniscata costante	ϖ {displaystyle {varpi} ${\varpi }$	π G = 4 2 π ( 1 4 ! ) 2 {displaystyle \pi \pi \G}=4{sqrt {\tfrac {2}{\pi}},({\tfrac {1}{4}}!)^{2}} $\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,({\tfrac {1}{4}}!)^{2}$	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} ${G}$	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}}}}}} ${\underset {Agm:\;Arithmetic-geometric\;mean}{{\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}}}$	(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)} $\zeta (6)$	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}}}... } ${\frac {\pi ^{6}}{945}}=\prod _{n=1}^{\infty }{\underset {p_{n}:\,{primo}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1{-}2^{-6}}}{\cdot }{\frac {1}{1{-}3^{-6}}}{\cdot }{\frac {1}{1{-}5^{-6}}}...$	Prod[n=1 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)}} ${\frac {1}{\zeta (2)}}$	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 } ${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)\dots$	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}}}}} ${\frac {\pi }{2{\sqrt {2}}}}$	∑ n = 1 ∞ ( - 1 ) ⌊ n - 1 2 ⌋ 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 - ... {\displaystyle \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} $\sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots$	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} ${F}$	∫ 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} $\int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	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	Radice quadrata del numero e	e {displaystyle {sqrt {e}} ${\sqrt {e}}$	∑ 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}}} $\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots$	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} ${i}$	- 1 = ln ( - 1 ) π e i π = - 1 {\displaystyle {\sqrt {-1}={frac {\ln(-1)}{\sqquadro \qquadro \mathrm {e} ^{i\,\pi\=-1} ${\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1$	sqrt(-1)	C
262537412640768743.999999999999250073	Costante di Hermite-Ramanujan	R {displaystyle {R} ${R}$	e π 163 {displaystyle e^{{pi {163}}}} $e^{\pi {\sqrt {163}}}$	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 $\gamma$	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}} ${\sqrt[{i}]{i}}=i^{-i}=i^{\frac {1}{i}}=(i^{i})^{-1}=e^{\frac {\pi }{2}}$	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 } $\alpha$	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}} ${\frac {\pi }{ln(2)}}={\frac {\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}{-}{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-\dots }{{\frac {1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}-\dots }}$	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} $th\,1$	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}} ${\frac {e-{\frac {1}{e}}}{e+{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}$	(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} ${C}_{CF}$	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}}} ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(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}} ${\frac {1}{e}}$	∑ 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} $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots$	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} $e$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots$	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 ! } $i\,!$	Γ ( 1 + i ) = i Γ ( i ) {\displaystyle \Gamma (1+i)=i\,\Gamma (i)} $\Gamma (1+i)=i\,\Gamma (i)$	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} ${}^{\infty }i$	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}} $\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	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	Modulo di infinito Tetrazione di i	{\an8}(*Circostanza) $\|{}^{\infty }i\|$	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} $\lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right\|$	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	Costante di Meissel-Mertens	M {displaystyle M} $M$	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)} $\lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)$ ..... 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 } $\omega$	⌊ 2 2 2 ⋅ ⋅ 2 ω ⌋ {displaystyle 【left\lfloor 2^{2^{2^{2^{cdot ^{cdot ^{2^{omega }}}}}}\right\rfloor } $\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\right\rfloor$ = primos: ‗displaystyle', ‗quadro'. ⌊ 2 2 2 ω ⌋ {displaystyle ）left\lfloor 2^{2^{2^{omega}}}destra\rfloor } $\left\lfloor 2^{2^{2^{\omega }}}\right\rfloor$ =16381, ... {displaystyle ）punti} $\dots$			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} $C_{Artin}$	∏ n = 1 ∞ ( 1 - 1 p n ( p n - 1 ) ) {\displaystyle \prod _{n=1}^{\infty}left(1-{frac {1}{p_{n}(p_{n}-1)}}right)} $\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)$ ...... 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} ${\delta }$	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)} $\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ 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})} $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {o}\quad x_{n+1}=\,a\sin(x_{n})$		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 } $\alpha$	lim n → ∞ d n d n + 1 {displaystyle \lim _{n\a6} a \infty }{frac {d_{n}}{d_{n+1}}}} $\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$		T	A006891	[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
5.97798681217834912266905331933922774	Madelung esagonale costante ₂	H 2 ( 2 ) {\displaystyle H_{2}(2)} $H_{2}(2)$	π ln ( 3 ) 3 {displaystyle \pi \ln(3){sqrt {3}} $\pi \ln(3){\sqrt {3}}$	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)} $\beta (3)$	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 } ${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\dots$	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} $B_{\,2}$	∑ ( 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} $\textstyle \sum {\underset {p,\,p+2:\,{primos}}{({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+\dots$			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} $B_{\,4}$	( 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 } ${\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22.4591577183610454734271522045437350	pi^e	π e {displaystyle \pi ^{e} $\pi ^{e}$	π e {displaystyle \pi ^{e} $\pi ^{e}$	pi^e		A059850	[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]
3.14159265358979323846264338327950288	Pi greco, costante di Archimede	π \displaystyle \più $\pi$	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}} $\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}$	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}} $e^{-e}$	e - e {\displaystyle e^{-e}} $e^{-e}$ ... 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} $i^{i}$	e - π 2 {{displaystyle e^{frac {-\pi}{2}} $e^{\frac {-\pi }{2}}$	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 } $\beta$	1 2 π {displaystyle {frac {1}{2{sqrt {{pi }}}}} ${\frac {1}{2{\sqrt {\pi }}}}$		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 } $\prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)\dots$	prod[n=1 a ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Inverso di Pi, Ramanujan	1 π {displaystyle {frac {1}{\pi}} ${\frac {1}{\pi }}$	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}}}} ${\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}}$		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}}} $W_{_{WE}}$	e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 {displaystyle {e^{{frac {\frac {\pi }8}{sqrt {\pi}}{42^{3/4}{({\frac {1}{4}}!)^{2}}}}} ${\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{42^{3/4}{({\frac {1}{4}}!)^{2}}}}$	(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 } $\Omega$	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 } $W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots$	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 $\gamma$	- 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}}} $-\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}$	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}}}}} ${\frac {\pi }{3{\sqrt {3}}}}$	∑ 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}{n{2n \scegliere n}}}=1-1... 1... 2... + 1... 4... 4... 4... 5... + 1... 7... 7... 8... 8... $\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$	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} ${\frac {2}{\pi }}$	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}} ${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
0.66016181584686957392781211001455577	Costante primaria gemella	C 2 {displaystyle C_{2} $C_{2}$	∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {displaystyle \prod _{p=3}^{infty }{frac {p(p-2)}{(p-1)^{2}}}} $\prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}$	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 $\lambda$				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)} $Ln(2)$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots$	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}} $I_{1}$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots$	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)} $\beta (1)$	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)} ${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	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}} ${\frac {\zeta (2)}{2}}$	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 } ${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots$	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} $C$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots$	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}} ${\sqrt[{12}]{2}}$	2 12 {displaystyle {sqrt[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	Zeta(04)	ζ 4 {displaystyle \zeta {4} $\zeta {4}$	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 } ${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+\dots$	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} $C_{Vi}$	lim n → ∞ \| a n \| 1 n {displaystyle \lim _{n\to \infty }\|a_{n}\|^{frac {1}{n}}} $\lim _{n\to \infty }\|a_{n}\|^{\frac {1}{n}}$			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)} $\zeta (3)$	∑ 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 \, } $\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots \,\!$	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}})} $\Gamma ({\tfrac {3}{4}})$	( − 1 + 3 4 ) ! { {\frac {\frac {3}{4}} a destra) ! } $\left(-1+{\frac {3}{4}}\right)!$	(-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	Costante di Favard	3 4 ζ ( 2 ) {displaystyle {\tfrac {3}{4}}\zeta (2)} ${\tfrac {3}{4}}\zeta (2)$	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 } ${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\dots$	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}} ${\sqrt[{3}]{2}}$	2 3 {displaystyle {sqrt[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	Il sogno del secondo anno ₂ J.Bernoulli	I 2 {displaystyle I_{2} $I_{2}$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}=1+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}+\dots$	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 } $\rho$	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 }}}}}}}}} ${\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+{\sqrt[{3}]{1+\cdots }}}}}}}}$		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}} ${\sqrt {2}}$	∏ 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)... } $\prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\left(1{+}{\frac {1}{1}}\right)\left(1{-}{\frac {1}{3}}\right)\left(1{+}{\frac {1}{5}}\right)...$	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}}} $e^{\frac {1}{e}}$	e 1 / e {\displaystyle e^{1/e}} $e^{1/e}$ ... 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}} $W_{2D}$	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}} $\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}$	(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	Prodotto Wallis	π / 2 {displaystyle \pi /2} $\pi /2$	∏ 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}} $\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$		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}} $E_{\,B}$	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! } $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!$	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 } $\varphi$	1 + 5 2 = 1 + 1 + 1 + 1 + 1 + ⋯ {displaystyle {frac {1+{sqrt {5}}{2}={sqrt {1+{sqrt {1+{sqrt {1+{sqrt {1+{punti }}}}}}}}} ${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(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)} $\zeta (\,2)$	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 } ${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	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 } $\sigma$	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 } ${\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots$		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}} ${\sqrt {3}}$	3 {displaystyle {sqrt {3}} ${\sqrt {3}}$	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} $R$	1 + 2 + 3 + 4 + ⋯ {displaystyle {sqrt {1+{sqrt {2+{sqrt {3+{sqrt {4+capitoli }}}}}}}}} ${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$			A072449	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
1.77245385090551602729816748334114518	Costante Carlson-Levin	Γ ( 1 2 ) {displaystyle \Gamma ({tfrac {1}{2}})} $\Gamma ({\tfrac {1}{2}})$	π = ( − 1 2 ) ! {displaystyle {sqrt {\i}=sinistra(-{frac {1}{2}}destra) !) } ${\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!$	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	Costante parabolica universale	P 2 {displaystyle P_{\2} $P_{\,2}$	ln ( 1 + 2 ) + 2 {displaystyle \ln(1+{sqrt {2})+{sqrt {2}}} $\ln(1+{\sqrt {2}})+{\sqrt {2}}$	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}} $\sigma _{\,Rr}$	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 }}}}}}}}} ${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(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 } $2\,\ln \,\gamma$	π 2 6 ln ( 2 ) {displaystyle {frac {\pi ^{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	radice quadrata di 2 pi greco	2 π {displaystyle {sqrt {2\pi} ${\sqrt {2\pi }}$	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}}}}} ${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}$	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}} $2^{\sqrt {2}}$	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}} $K_{\,0}$	∏ 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}} $\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	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	Costante di Khinchin-Lévy	γ γ γ γ γ γ γ γ γ γ γ $\gamma$	e π 2 / ( 12 ln 2 ) {displaystyle e^{{pi ^{2}/(12\ln 2)}} $e^{\pi ^{2}/(12\ln 2)}$	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 } $\Psi$	∑ 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 } $\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$			A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4.13273135412249293846939188429985264	Radice di 2 e pi	2 e π {displaystyle {sqrt {2e\pi} ${\sqrt {2e\pi }}$	2 e π {displaystyle {sqrt {2e\pi} ${\sqrt {2e\pi }}$	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} $2^{\,e}$	2 e {displaystyle 2^{e}} $2^{e}$	2^e			[6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...]
9.86960440108935861883449099987615114	Pi al quadrato	π 2 {displaystyle \pi ^{2}} $\pi ^{2}$	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 } $6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots$	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} $e^{\pi }$	∑ 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 } $\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	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,...]

Pagine correlate

Funzione costante
Elenco di simboli matematici

Bibliografia online

Enciclopedia on line delle sequenze di interi (OEIS)
Simon Plouffe, Tabelle delle costanti
La pagina di numeri, costanti matematiche e algoritmi di Xavier Gourdon e Pascal Sebah
MathConstants

Domande e risposte

D: Che cos'è una costante matematica?

R: Una costante matematica è un numero che ha un significato speciale per i calcoli.

D: Qual è un esempio di costante matematica?

R: Un esempio di costante matematica è ً, che rappresenta il rapporto tra la circonferenza di un cerchio e il suo diametro.

D: Il valore di ً è sempre lo stesso?

R: Sì, il valore di ً è sempre lo stesso per qualsiasi cerchio.

D: Le costanti matematiche sono numeri integrali?

R: No, le costanti matematiche sono solitamente numeri reali, non integrali.

D: Da dove provengono le costanti matematiche?

R: Le costanti matematiche non derivano da misurazioni fisiche come le costanti fisiche.