Stała matematyczna

Stała matematyczna to liczba, która ma specjalne znaczenie dla obliczeń. Na przykład, stała π (wymawiana jako "pie") oznacza stosunek obwodu koła do jego średnicy. Wartość ta jest zawsze taka sama dla każdego okręgu. Stała matematyczna jest często interesującą nas liczbą rzeczywistą, niecałkowitą.

W przeciwieństwie do stałych fizycznych, stałe matematyczne nie pochodzą z pomiarów fizycznych.

Kluczowe stałe matematyczne

Poniższa tabela zawiera kilka ważnych stałych matematycznych:

Nazwa	Symbol	Wartość	Znaczenie
Pi, stała Archimedesa lub liczba Ludoph'a	π	≈3.141592653589793	Liczba transcendentalna, która jest stosunkiem długości obwodu koła do jego średnicy. Jest to również pole koła jednostkowego.
E, stała Napiera	e	≈2.718281828459045	Liczba transcendentalna, która jest podstawą logarytmu naturalnego, czasami nazywana "liczbą naturalną".
Złota proporcja	φ	5 + 1 2 ≈ 1.618 {{displaystyle {{sqrt {5}}+1}{2}}}approx 1.618} ${\frac {{\sqrt {5}}+1}{2}}\approx 1.618$	Jest to wartość większej wartości podzielonej przez mniejszą wartość, jeśli jest ona równa wartości sumy wartości podzielonej przez większą wartość.
Pierwiastek kwadratowy z 2, stała Pitagorasa	2 {{displaystyle {{sqrt {2}}} ${\sqrt {2}}$	≈ 1.414 {styl wyświetlania ≈ około 1.414} $\approx 1.414$	Liczba irracjonalna, która jest długością przekątnej kwadratu o boku długości 1. Liczba ta nie może być zapisana jako ułamek.

Stałe i szeregi

Poniższa tabela zawiera listę stałych i szeregów w matematyce, z następującymi kolumnami:

Wartość: Wartość liczbowa stałej.
LaTeX: Wzór lub seria w formacie TeX.
Wzór: Do użytku w programach takich jak Mathematica lub Wolfram Alpha.
OEIS: Link do On-Line Encyclopedia of Integer Sequences (OEIS), gdzie stałe są dostępne z większą ilością szczegółów.
Ułamek ciągły: W postaci prostej [do liczby całkowitej; frac1, frac2, frac3, ...] (w nawiasach, jeśli okresowy)
Typ:

R - liczba rzeczywista
I - liczba irracjonalna
T - liczba transcendentalna
C - Liczba złożona

Zauważ, że lista może być odpowiednio uporządkowana poprzez kliknięcie na tytuł nagłówka na górze tabeli.

Wartość	Nazwa	Symbol	LaTeX	Formuła	Typ	OEIS	Frakcja kontynuowana
3.24697960371746706105000976800847962	Srebro, stała Tutte-Beraha	ς { {displaystyle \varsigma } $\varsigma$	2 + 2 cos ( 2 π / 7 ) = 2 + 2 + 7 + 7 7 + 7 7 + ⋯ 3 3 3 1 + 7 + 7 + 7 7 + ⋯ 3 3 3 {tekstylia 2+2 cos ( 2 π / 7 ) =tekstylia 2+{frac {2+{sqrt[{3}]{7+7{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	Niezmienny Paryż	C P a {{Pa}} $C_{Pa}$	∏ n = 2 ∞ 2 φ φ + φ n , φ = F i {displaystyle \prod _{n=2}^{infty }{frac {2}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 zagnieżdżony rodnik R5	R 5 {{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 {5+{sqrt {5+{sqrt {5+{sqrt {5}}} }}}}}}}}}}}}}}};=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	Pierwiastek kwadratowy z 5, suma Gaussa	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 ∀ forall ∀ n=5,\displaystyle \ suma _{k=0}^{n-1}e^{frac {2k^{2}\i}{n}}=1+e^{frac {2\i}{5}}+e^{frac {8\i}{5}}+e^{frac {18\i}{5}}+e^{frac {32\i}{5}} $\scriptstyle \forall \,n=5,\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	Suma[k=0 do 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 ) ! {{displaystyle 4}}left({{frac {1}{4}}}prawostronny)!={left(-{frac {3}{4}}}prawostronny)! } $4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	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	MRB constant, Marvin Ray Burns	C M R B {{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}}} } } } $\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,\dots$	Suma[n=1 do ∞]{(-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	Stała Keplera-Bouwkampa	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({\nrac {\n}}prawa)= \cos \left({\nrac {\n}prawa)\cos \left({\nrac {\n}{4}}prawa)\nos \nleft({\nrac {\n}}prawa)\cos \n Left({\nrac {\n}prawa)\dots } $\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)\dots$	prod[n=3 do ∞]{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) Funkcja G-Barnesa	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 = { {prod _{n=1}^{infty }}}{1+{tfrac {1}{n}}}}= \prod _{n=0}^{infty }}left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \i0}}prawo)^{{frac {1}{n \i0}}}=} $\prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}=$ ( 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 … 2^{3}}{1}}prawica)^{1/4}left({ {frac {2^{4}}{1}}}{1}}}prawica)^{1/5}}prawica} } $\textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/5}\dots$	Prod[n=1 do ∞]{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	Stała Glaishera-Kinkelina	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}}}suma ^{infty }1)}=e^{{{{frac {1}{8}}-{{{frac {1}{2}}}suma ^limitów _{n=0}^{infty }{{{frac {1}{n+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	Stała stożkowa Schwarzschilda	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!}}+ kropki } $\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\dots$	Suma[n=0 do ∞]{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, itd.
1.01494160640965362502120255427452028	Stała Giesekinga	G G i {{G_{Gi}}} ${G_{Gi}}$	3 3 4 ( 1 - ∑ n = 0 ∞ 1 ( 3 n + 2 ) 2 + ∑ n = 1 ∞ 1 ( 3 n + 1 ) 2 ) = {{displaystyle {{frac {{sqrt {3}}}{4}}}left(1-^sum _{n=0}^{infty }} + ^sum _{n=1}^{infty }} {{infrac {1}{(3n+1)^{2}}}}} right)=} ${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ 3 3 4 ( 1 − 1 2 2 + 1 4 2 − 1 5 2 + 1 7 2 − 1 8 2 + 1 10 2 ± … ) { {{displaystyle }textstyle {{sqrt {3}}{4}}}left(1-{{sqrt {1}{2^{2}}}+{sqrt {1}{4^{2}}}-{sqrt {1}{5^{2}}}+{sqrt {1}{7^{2}}}-{sqrt {1}{8^{2}}}+{sqrt {1}{10^{2}}}}}}pm } $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \dots \right)$ .		T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
2.62205755429211981046483958989111941	Lemniscata stała	ϖ {{displaystyle {{varpi }} ${\varpi }$	π G = 4 2 π ( 1 4 ! ) 2 {{displaystyle {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	Stała Gaussa	G {{displaystyle {G}} ${G}$	1 a g m ( 1 , 2 ) = 4 2 ( 1 4 ! ) 2 π 3 / 2 A g m : A r y t h m e t i c - g e o m e t r i c m e a n {displaystyle {}underset {Agm:™;Arytmetyczno-geometryczna};średnia}{{frac {1}{mathrm {agm} (1,1}{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 ) { {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{-}2^{-6}}}}{{cdot }{{frac {1}{1{-}3^{-6}}}}{{cdot }{{frac {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 do ∞] {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	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}:{{primo}}{}{}left(1-{prac {1}{{p_{n}}^{2}}}}}}}}{=}textstyle {{left(1{-}{prac {1}{2^{2}}}}}}}}} {{left(1{-}{prac {1}{3^{2}}}}}}}}}}}}}}} {{left(1{-}{prac {1}{5^{2}}}}}}}}}}}} kropki } ${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{primo}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)\dots$	Prod{n=1 do ∞} (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	Stosunek kwadratu i okręgów wpisanych lub obwiedzionych	π 2 2 {displaystyle {frac {pi }{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 }}suma _{n=1}^{infty }} {{frac {(-1)^{floor {{n-1}{2}}}}}{2n+1}}={{frac {1}{1}}+{{frac {1}{3}}-{{frac {1}{5}}-{{frac {1}{7}}+{{frac {1}{9}}+{{frac {1}{11}}}} kropki }}. $\sum _{n=1}^{\infty }{\frac {(-1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-\dots$	suma[n=1 do ∞]{(-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	Stała Fransén-Robinsona	F {{displaystyle {F}} ${F}$	∫ 0 ∞ 1 Γ ( x ) d x . = e + ∫ 0 ∞ e - x π 2 + ln 2 x d x { ∫ 0 ∞ e - x π 2 + ln 2 x d x { ∫ 0 ∞ ∞ ∞ int _{0}^{infty }{ ↪Sm_221}{1}{Gamma (x)}}},dx.=e+ int _{0}^{infty }{ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ↪Sm_221}{ ln 2 x d 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 do ∞] {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	Pierwiastek kwadratowy z liczby e	e {{displaystyle {{sqrt {{e}}} ${\sqrt {e}}$	∑ n = 0 ∞ 1 2 n n ! = ∑ n = 0 ∞ 1 ( 2 n ) ! !	suma[n=0 do ∞]{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	Liczba urojona	i {{displaystyle {i}} ${i}$	- 1 = ln ( - 1 ) π e i π = - 1 {{displaystyle {{sqrt {-1}}={frac {{ln(-1)}{pi }}} ^{iquad ^mathrm {e}} ^{i},^pi }=-1}. ${\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1$	sqrt(-1)	C
262537412640768743.999999999999250073	Stała Hermite'a-Ramanujana	R {{displaystyle {R}} ${R}$	e π 163 {displaystyle e^{pi {sqrt {163}}}} $e^{\pi {\sqrt {163}}}$	e^(π sqrt(163))	T	A060295	[262537412640768743;1,1333462407511,1,8,1,1,5,...]
4.81047738096535165547303566670383313	John niezmienny	γ { {displaystyle \gamma } $\gamma$	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	Constante de Van der Pauw	α { {displaystyle \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}}}={{{suma _{n=0}^{infty }}}{{{frac {4(-1)^{n}}{2n+1}}}}{{{suma _{n=1}^{infty }} {{{frac {(-1)^{n+1}}}{n}}}}={{{suma _{n=0}^{{infty }}}{{{frac {4}{1}}}{-{{frac {4}{3}}{+}{{frac {4}{5}}{-}{{frac {4}{7}}{+}{{frac {4}{9}}-}dots }} ${\frac {\pi }{ln(2)}}={\frac {\sum _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}{-}{\frac {4}{3}}{+}{\frac {4}{5}}{-}{\frac {4}{7}}{+}{\frac {4}{9}}-\dots }{{\frac {1}{1}}{-}{\frac {1}{2}}{+}{\frac {1}{3}}{-}{\frac {1}{4}}{+}{\frac {1}{5}}-\dots }}$	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	Tangens hiperboliczny (1)	t h 1 {styl wyświetlania th,1} $th\,1$	e - 1 e e + 1 e = 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	ciąg dalszy Stała frakcji	C C F {{C}_{CF}} ${C}_{CF}$	J 1 ( 2 ) J 0 ( 2 ) F u n k c j a J k ( ) B e s s e l = ∑ n = 0 ∞ n 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}(){Bessela}}{{underset {Function}}{{frac {J_{1}(2)}{J_{0}(2)}}}}={{frac {{suma \limits _{n=0}^{infty }{{frac {n}{n!n!}}}{}suma \limits _{n=0}^{infty }{ {{frac {1}{n!n!}}}}= {{{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}}}+{{{{}}}}}}}. ${\underset {J_{k}(){Bessel}}{\underset {Function}{\frac {J_{1}(2)}{J_{0}(2)}}}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}={\frac {{\frac {0}{1}}+{\frac {1}{1}}+{\frac {2}{4}}+{\frac {3}{36}}+{\frac {4}{576}}+\dots }{{\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{4}}+{\frac {1}{36}}+{\frac {1}{576}}+\dots }}$	(suma {n=0 do inf} n/(n!n!)) /(suma {n=0 do 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	Odwrotna stała Napiera	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 }}suma _{n=0}^{infty }}={{{frac {1}{0!}}-{{{frac {1}{1!}}+{{frac {1}{2!}}-{{{frac {1}{3!}}+{{{frac {1}{4!}}-{{{frac {1}{5!}}+kropki }}. $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\dots$	suma[n=2 do ∞]{(-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,...] = [0;2,1,(1,2p,1)], p∈ℕ
2.71828182845904523536028747135266250	Stała 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}{0!}}+{{frac {1}{1!}}+{{frac {1}{2!}}+{{frac {1}{3!}}+{{frac {1}{4!}}+{{frac {1}{5!}}+{cdots }}. $\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+{\frac {1}{5!}}+\cdots$	Suma[n=0 do ∞]{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	Czynnik i	i ! {{displaystyle i! } $i\,!$	Γ ( 1 + i ) = i Γ ( i ) { Γ (1+i)=i, Γ (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	Nieskończony Tetracja i	∞ i {{displaystyle {}^{infty }i} ${}^{\infty }i$	lim n → ∞ n i = lim n → ∞ i i i ⋅ ⋅ i ⏟ n {{displaystyle \\lim _{n\ do \infty }{^{n}i= \lim _{n\ do \infty }{underbrace {i^{i^{cdot ^{i}}}}} _{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	Moduł nieskończoności Tetracja z i	∞ i \| {displaystyle \|{}^{infty }i\|} $\|{}^{\infty }i\|$	lim n → ∞ \| n i \| = \| lim n → ∞ i i i ⋅ ⋅ i ⏟ n \| {displaystyle \lim _{n}to \infty } \left\|{}^{n}i\right\|= \left\|lim _{n}to \infty } \underbrace {i^{i^{cdot ^{i}}}}} prawo $\lim _{n\to \infty }\left\|{}^{n}i\right\|=\left\|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right\|$	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	Stała Meissel-Mertens	M {{displaystyle M}} $M$	lim n → ∞ ( ∑ p ≤ n 1 p - ln ( ln ( n ) ) ) { {displaystyle \lim _{n \rightarrow \infty } \left(\sum _{p \leq n}{\frac {1}{p}}- \ln(\n(n))\right)} $\lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)$ ..... p: primes			A077761	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,...]
1.9287800...	Stała Wrighta	ω { {displaystyle ™omega } $\omega$	{{displaystyle \\quad } ⌊ $\quad$ 2 ω ⌋ {displaystyle ⌊ 2 ω ⌋ {displaystyle ⌊ 2 ω ⌋ {displaystyle ⌊ 2 ω ⌋ ⌋ ⌊ 2 ω ⌋ ^{2^{omega }}right ⌊ } $\left\lfloor 2^{\omega }\right\rfloor$ =3, ⌊ 2 2 ω ⌋ {displaystyle ⌊ 2 ω ⌋ ^^^omega } $\left\lfloor 2^{2^{\omega }}\right\rfloor$ =13, {displaystyle \u0026apos; } $\dots$			A086238	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
0.37395581361920228805472805434641641	Stała Artina	C A r t i n {{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	Stała Feigenbauma δ	δ {displaystyle {delta }} ${\delta }$	x n + 1 = a x n ( 1 - x n ) o x n + 1 = a sin ( x n ) { {displaystyle \scriptstyle x_{n+1}= a 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	Stała Feigenbauma α	α { {displaystyle \alpha } $\alpha$	lim n → ∞ d n d n + 1 {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	Sześciokątny Madelung Stała 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 ) {styl wyświetlania βbeta (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}}}=suma _{n=1}^{infty }}{{{frac {-1^{n+1}}{(-1+2n)^{3}}}={{{frac {1}{1^{3}}}{-}{}{}{1}{3^{3}}}}{+}{{frac {1}{5^{3}}}}{-}{}{}}}}. ${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\dots$	Suma[n=1 do ∞]{(-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 stała ₂ = Σ odwrotność podwójnych liczb pierwszych	B 2 {{displaystyle B_{}} $B_{\,2}$	{p}}{({{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}})+ kropki }. $\textstyle \sum {\underset {p,\,p+2:\,{primos}}{({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+\dots$			A065421	[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
0.870588379975	Brun stała ₄ = Σ odwrotność liczby pierwszej bliźniaczej	B 4 {displaystyle B_{}} $B_{\,4}$	( 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 {p,p+2,p+4,p+6:{primes}}{}left({{tfrac {1}{5}}+{tfrac {1}{7}}+{tfrac {1}{11}}+{tfrac {1}{13}}}prawica)}}+left({{tfrac {1}{11}}+{tfrac {1}{13}}+{tfrac {1}{17}}+{tfrac {1}{19}}}prawica)} + kropki } } ${\underset {p,\,p+2,\,p+4,\,p+6:\,{primes}}{\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
22.4591577183610454734271522045437350	pi^e	π e {{displaystyle \i ^{e}} $\pi ^{e}$	π e {{displaystyle \i ^{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, stała Archimedesa	π { {displaystyle \i } $\pi$	lim n → ∞ 2 n 2 - 2 + 2 + ⋯ + 2 ⏟ n {{displaystyle }lim _{n do ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 2 n 2 - 2 + 2 + ⋯ + 2 ⏟ n _{n}} $\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\dots +{\sqrt {2}}}}}}}} _{n}$	Suma[n=0 do ∞]{(-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}} $e^{-e}$ ... Dolna granica tetracji		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 {\i0} $i^{i}$	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	Stała Bernsteina	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 i 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}}}}}}prawa)= \left(1{-}{}frac {1}{2^{1}}}}prawa)\left(1{-}{}frac {1}{2^{2}}}}prawa)\left(1{-}{}{}frac {1}{2^{3}}}}prawa)\dots } $\prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)\dots$	prod[n=1 do ∞]{1-1/2^n}		A048651
0.31830988618379067153776752674502872	Odwrotność liczby 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}}}suma _{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	Stała Weierstraß	W W E {{_{WE}}} $W_{_{WE}}$	e π 8 π 4 ∗ 2 3 / 4 ( 1 4 ! ) 2 { {displaystyle { {e^{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	Stała omega	Ω {displaystyle ™Omega } $\Omega$	W ( 1 ) = ∑ n = 1 ∞ ( - n ) n - 1 n ! = 1 - 1 + 3 2 - 8 3 + 125 24 - ... {displaystyle W(1)= ∑ suma _{n=1}^{infty } {{frac {(-n)^{n-1}}{n!}}=1{-}1{+}{}{}frac {3}{2}}{-}{}{}frac {8}{3}}{+}{125}{24}}}- kropki } $W(1)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=1{-}1{+}{\frac {3}{2}}{-}{\frac {8}{3}}{+}{\frac {125}{24}}-\dots$	suma[n=1 do ∞]{(-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	Liczba Eulera	γ { {displaystyle \gamma } $\gamma$	- ψ ( 1 ) = ∑ n = 1 ∞ ∑ k = 0 ∞ ( - 1 ) k 2 n + k {suma _{n=1}^{infty }}sum _{k=0}^{infty }} {frac {(-1)^{k}}{2^{n}+k}}} $-\psi (1)=\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}$	suma[n=1 do ∞]\|suma[k=0 do ∞]{((-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 Dirichleta	π 3 3 {displaystyle {frac {pi }{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 }}=1-.{{frac {1}{2}}+{{frac {1}{4}}-{{frac {1}{5}}}+{{frac {1}{7}}-{{frac {1}{8}}}+{cdots } $\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$	Suma[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, François Viète	2 π {{displaystyle {{frac {2}{{pi }}} ${\frac {2}{\pi }}$	2 2 ⋅ 2 + 2 2 ⋅ 2 + 2 + 2 2 ⋯ {{displaystyle}} {{sqrt {2+{sqrt {2}}}}{2}}}}} {{sqrt {2+{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	Podwójna stała pierwszorzędna	C 2 {{2}} $C_{2}$	∏ p = 3 ∞ p ( p - 2 ) ( p - 1 ) 2 {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 do ∞]{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	Stała graniczna Laplace'a	λ {displaystyle ™lambda } $\lambda$				A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,...]
0.69314718055994530941723212145817657	Logarytm de 2	L n ( 2 ) {przykład 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 } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots$	Suma[n=1 do ∞]{(-1)^(n+1)/n}	T	A002162	[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,...]
0.78343051071213440705926438652697546	Sen Zofii ₁ J.Bernoulli	I 1 {{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}}}}+{dots } $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}=1-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+\dots$	Suma[ -(-1)^n /n^n]	T	A083648	[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,...]
0.78539816339744830961566084581987572	Dirichlet beta(1)	β ( 1 ) {styl wyświetlania βbeta (1)} $\beta (1)$	π 4 = ∑ n = 0 ∞ ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - ⋯ {{displaystyle {{frac {{pi}}}}={suma _{n=0}}^{infty }} {{frac {(- 1)^{n}}{2n+1}}={{frac {1}{1}}-{{frac {1}{3}}+{frac {1}{5}}-{{frac {1}{5}}-{frac {1}{1}}}}1)^{n}}{2n+1}}={{frac {1}{1}}-{{frac {1}{3}}+{{frac {1}{5}}-{{frac {1}{7}}+{{frac {1}{9}}}-{cdots } ${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	Suma[n=0 do ∞]{(-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	Podróżujący sprzedawca Nielsen-Ramanujan	ζ ( 2 ) 2 {{displaystyle {{frac {{zeta (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}}}=suma _{n=1}^{infty }} {{frac {(-1)^{n+1}}}{n^{2}}}={{frac {1}{1}{1^{2}}}}{-}{}{1}{2^{2}}}}{+}{{frac {1}{3^{2}}}}{-}{}{1}{4^{2}}}}{+}{{frac {1}{5^{2}}}}- kropki } ${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}-\dots$	Suma[n=1 do ∞]{((-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	Stała katalońska	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 \a_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 } $\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+\cdots$	Suma[n=0 do ∞]{(-1)^n/(2n+1)^2}	I	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,...]
1.05946309435929526456182529494634170	Stosunek odległości między półtonami	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}}}=suma _{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 }}. ${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+\dots$	Suma[n=1 do ∞]{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 ...	Stałość Viswanaths	C V i {{Vi}} $C_{Vi}$	lim n → ∞ \| a n \| 1 n {{displaystyle }\|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	Apéry constant	ζ ( 3 ) { {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 }} {1}{n^{3}}}={{{frac {1}{1^{3}}}+{{{frac {1}{2^{3}}}}+{{{frac {1}{3^{3}}}+{{{frac {1}{4^{3}}}+{{{frac {1}{5^{3}}}}+{{cdots \i0},\! } $\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots \,\!$	Suma[n=1 do ∞]{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 ) ! { {displaystyle \left(-1+{{frac {3}{4}}}right)! } $\left(-1+{\frac {3}{4}}\right)!$	(-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	Stała Favarda	3 4 ζ ( 2 ) { {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}}}=suma _{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 }}. ${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\dots$	suma[n=1 do ∞]{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	Pierwiastek sześcienny z 2, stała Deliana	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	Marzenie nastolatki ₂ J.Bernoulli	I 2 {{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}}}}+{dots } $\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}=1+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{5}}}+{\frac {1}{6^{6}}}+\dots$	Suma[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	Numer z tworzywa sztucznego	ρ {displaystyle ™rho } $\rho$	1 + 1 + 1 + 1 + ⋯ 3 3 3 3 {{displaystyle {{sqrt[{3}]{1+{sqrt[{3}]{1+{sqrt[{3}]{1+{sqrt[{3}]{1+{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	Pierwiastek kwadratowy z 2, stała Pitagorasa	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}}= \left(1{+}{frac {1}{1}}}prawica)\left(1{-}{frac {1}{3}}}prawica)\left(1{+}{frac {1}{5}}}prawica)... } $\prod _{n=1}^{\infty }1+{\frac {(-1)^{n+1}}{2n-1}}=\left(1{+}{\frac {1}{1}}\right)\left(1{-}{\frac {1}{3}}\right)\left(1{+}{\frac {1}{5}}\right)...$	prod[n=1 do ∞]{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	Liczba Steinera	e 1 e {{displaystyle e^{frac {1}{e}}} $e^{\frac {1}{e}}$	e 1 / e {{displaystyle e^{1/e}} $e^{1/e}$ ... Górna granica tetracji			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 constant	W 2 D {{2D}} {{displaystyle W_{2D}} $W_{2D}$	lim n → ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 3 2 { {displaystyle ∞ ∞ ∞ ∞ ∞ ( f(n))^{n^{-2}}= ∞ ∞ ∞ ∞ ∞ ( f ( n ) ) n - 2 = ( 4 3 ) 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	Produkt Wallis	π / 2 {przyp. tłum.} $\pi /2$	∏ 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 ⋯ { {prod _{n=1}^{infty }}left({{frac {4n^{2}}{4n^{2}-1}} prawo)={{frac {2}{1}}}prawda}} {{frac {2}{3}}}prawda} {{frac {4}{3}}}prawda} {{frac {4}{5}}}prawda} {{frac {6}{5}}}prawda} {{frac {6}{7}}}prawda} {{frac {8}{7}}}prawda} {{frac {8}{9}}}prawda} } $\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$		T	A019669	[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1...]
1.60669515241529176378330152319092458	Stała Erdősa-Borweina	E B {{displaystyle E_{,B}} $E_{\,B}$	∑ n = 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 \},\}. } $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}+{\frac {1}{3}}+{\frac {1}{7}}+{\frac {1}{15}}+\cdots \,\!$	suma[n=1 do ∞]{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, złota proporcja	φ {displaystyle \\varphi } $\varphi$	1 + 5 2 = 1 + 1 + 1 + 1 + ⋯ {displaystyle {{displayfrac {1+{sqrt {5}}}{2}}={sqrt {1+{sqrt {1+{sqrt {1+{sqrt {1+{sqrt {1+{sqrt {1+}}} }}}}}}}}} ${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(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 ) { ζ ( 2 ) { ζ ( 2 ) { ζ ( 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}}}= suma {{n=1}}^{infty }}={{{frac {1}{n^{2}}}+{{{frac {1}{2^{2}}}+{{{frac {1}{3^{2}}}+{{{frac {1}{4^{2}}}}+{{cdots }} ${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	Suma[n=1 do ∞]{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	Stała rekurencji kwadratowej Somosa	σ { {displaystyle \sigma } $\sigma$	1 2 3 ⋯ = 1 1 / 2 ; 2 1 / 4 ; 3 1 / 8 ⋯ {displaystyle { 1{sqrt {1{sqrt {2{sqrt {3}} }}}}}}=1^{1/2};2^{1/4};3^{1/8}}} } ${\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2};2^{1/4};3^{1/8}\cdots$		T	A065481	[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
1.73205080756887729352744634150587237	Stała Teodora	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	Liczba Kasnera	R {{displaystyle R}} $R$	1 + 2 + 3 + 4 + ⋯ {displaystyle {{sqrt {1+{sqrt {2+{sqrt {3+{sqrt {4+}} }}}}}}}}} ${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$			A072449	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
1.77245385090551602729816748334114518	Stała Carlson-Levin	Γ ( 1 2 ) {{displaystyle \Gamma ({tfrac {1}{2}}})} $\Gamma ({\tfrac {1}{2}})$	π = ( − 1 2 ) ! { {displaystyle { {sqrt {pi }}=left(-{frac {1}{2}}}right)! } ${\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!$	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	Uniwersalna stała paraboliczna	P 2 {{displaystyle P_{}} $P_{\,2}$	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	Numer z brązu	σ R r {{displaystyle {sigma _{,Rr}} $\sigma _{\,Rr}$	3 + 13 2 = 1 + 3 + 3 + 3 + ⋯ {displaystyle {{displayfrac {3+{sqrt {13}}}{2}}=1+{sqrt {3+{sqrt {3+{sqrt {3+{sqrt {3+{sqrt {3+{sqrt {3+}}} }}}}}}}}} ${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(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	Stała Lévy'ego2	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	pierwiastek kwadratowy z 2 pi	2 π {{displaystyle {{sqrt {2}pi }} ${\sqrt {2\pi }}$	2 π = lim n → ∞ n ! e n n n n {{sqrt {2}pi }}=lim _{n do \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	Stała Gelfonda-Schneidera	G G S {{displaystyle G_{{{{}}}} $G_{_{\,GS}}$	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	Stała 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 \over n(n+2)}}}right]^{ln n/{ln 2}} $\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	prod[n=1 do ∞]{(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	Stała Chinchina-Lévy'ego	γ { {displaystyle \gamma } $\gamma$	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	odwrotna stała Fibonacciego	Ψ {displaystyle ťPsi } $\Psi$	∑ n = 1 ∞ 1 F n = 1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1 13 + ⋯ {{displaystyle \sum _{n=1}^{infty }} {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 } $\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$			A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
4.13273135412249293846939188429985264	Pierwiastek z 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	Stała Froda	2 e {{displaystyle 2^{,e}} $2^{\,e}$	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 podniesione do kwadratu	π 2 {{displaystyle \i ^{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 Suma[n=1 do ∞]{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	Stała Gelfonda	e π {{displaystyle e^{pi }} $e^{\pi }$	∑ n = 0 ∞ π n n ! = π 1 1 + π 2 2 ! + π 3 3 ! + π 4 4 ! + ⋯ { {displaystyle \sum _{n=0}^{infty }}={{{frac {{pi ^{1}}{1}}}+{{{frac {{pi ^{2}}{2!}}+{{{frac {{{3}}{3!}}+{{{frac {{pi ^{4}}{4!}}+{cdots } $\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	Suma[n=0 do ∞]{(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]

Powiązane strony

Funkcja stała
Lista symboli matematycznych

Bibliografia online

On-Line Encyclopedia of Integer Sequences (OEIS)
Simon Plouffe, Tablice stałych
Strona Xaviera Gourdona i Pascala Sebah'a z liczbami, stałymi matematycznymi i algorytmami
MathConstants

Pytania i odpowiedzi

P: Co to jest stała matematyczna?

O: Stała matematyczna to liczba, która ma specjalne znaczenie dla obliczeń.

P: Jaki jest przykład stałej matematycznej?

A: Przykładem stałej matematycznej jest ً, która oznacza stosunek obwodu koła do jego średnicy.

P: Czy wartość ً jest zawsze taka sama?

O: Tak, wartość ً jest zawsze taka sama dla każdego koła.

P: Czy stałe matematyczne są liczbami całkowitymi?

O: Nie, stałe matematyczne są zazwyczaj liczbami rzeczywistymi, niecałkowitymi.

P: Skąd się biorą stałe matematyczne?

O: Stałe matematyczne nie pochodzą z pomiarów fizycznych, tak jak stałe fizyczne.