Anexo:Constantes matemáticas , la enciclopedia libre

-0,68400 03894 37932 129 i ^{[Ow 2]}​

±1,33723 57014 30689 40 i ^{[Ow 4]}​

${\displaystyle \lim _{n\rightarrow \infty }}$

${\displaystyle f(x)=\underbrace {\log(\log(\log(\log(\cdots \log(\log(x))))))\,\!} \atop {\log _{s}{\text{ anidados n veces}}}}$

Para un valor inicial de x distinto a 0, 1, e, e^e, e^(e^e), etc.

${\displaystyle \sum _{n=2}^{\infty }{\frac {1}{\mu (n)!}}{\color {white}....\color {black}}}$

μ(n) es el número más pequeño por el que μ(n)! es divisible por n

${\displaystyle 1=\!\sum _{n=1}^{\infty }{\frac {t_{k}}{q^{k}}}\qquad \scriptstyle {\text{Raiz real de}}\displaystyle \prod _{n=0}^{\infty }\!\left(\!1{-}{\frac {1}{q^{2^{n}}}}\!\right)\!{+}{\frac {q{-}2}{q{-}1}}=0}$

t _k = Sucesión de Thue-Morse

${\displaystyle \gamma +\int _{0}^{x}{\frac {\cosh t-1}{t}}\,dt}$

${\displaystyle \scriptstyle \gamma \,{\text{= Constante de Euler–Mascheroni = 0,5772156649...}}}$

${\displaystyle {\sqrt {2+{\sqrt {2}}}}\;=\lim _{n\rightarrow \infty }c_{n}^{1/n}}$

La menor raíz real de ${\displaystyle :\;x^{4}-4x^{2}+2=0}$

La menor raíz real de ${\displaystyle :\;\;4x^{4}{-}28x^{3}{-}7x^{2}{+}16x{+}16=0}$

${\displaystyle \sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}}$

${\displaystyle {t_{n}}}$

donde ${\displaystyle \tau (x)=\sum _{n=0}^{\infty }(-1)^{t_{n}}\,x^{n}=\prod _{n=0}^{\infty }(1-x^{2^{n}})}$

${\displaystyle {\frac {C}{\pi }}}$

C=Cte Catalan

${\displaystyle \lim _{n\to \infty }1-{\frac {!n}{n!}}=\lim _{n\to \infty }P(n)=\int _{0}^{1}e^{-x}dx=1-{\frac {1}{e}}=}$

${\displaystyle \sum \limits _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{1!}}-{\frac {1}{2!}}+{\frac {1}{3!}}-{\frac {1}{4!}}+{\frac {1}{5!}}-{\frac {1}{6!}}+\cdots }$

${\displaystyle \lim _{n\to \infty }{\frac {F_{n}(x)-\ln(1-x)}{(-\lambda )^{n}}}=\Psi (x),}$

donde ${\displaystyle \Psi (x)}$ es una función analítica tal que ${\displaystyle \Psi (0)\!=\!\Psi (1)\!=\!0}$.

${\displaystyle 1{+}{\frac {1}{2}}{+}{\frac {1}{3}}{+}\cdots {+}{\frac {1}{9}}{+}{\frac {1}{11}}{+}\cdots {+}{\frac {1}{19}}{+}{\frac {1}{21}}{+}\cdots {+}\,{\text{etc.}}}$

${\displaystyle {+}{\frac {1}{99}}{+}{\frac {1}{111}}{+}\cdots {+}{\frac {1}{119}}{+}{\frac {1}{121}}{+}\cdots \;\;{\overset {Excluidos\;los}{\underset {contienen\;ceros.}{\scriptstyle denominadores\;que}}}}$

${\displaystyle x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ para }}n=1,2,3,\ldots }$

La constante de Foias es el único número real tal que si x₁ = α, entonces la secuencia diverge a ∞. Cuando x₁ = α, ${\displaystyle \,\lim _{n\to \infty }x_{n}{\tfrac {\log n}{n}}=1}$

${\displaystyle \displaystyle {\frac {{\sqrt {21}}+1}{2}}=\scriptstyle \,{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5+\cdots }}}}}}}}}}\;}$

${\displaystyle =1+\,\scriptstyle {\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-\cdots }}}}}}}}}}\;}$

${\displaystyle {\frac {{\sqrt {17}}-1}{2}}=\,\scriptstyle {\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+\cdots }}}}}}}}}}}}\,\,-1}$

${\displaystyle =\,\scriptstyle {\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-\cdots }}}}}}}}}}}}\textstyle }$

${\displaystyle \lim _{k\to \infty }\left|{\frac {q_{k+1}}{q_{k}}}\right\vert \quad \scriptstyle {\text{donde:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty }q_{k}x^{k}}$

${\displaystyle P(x)=\!\sum _{k=1}^{\infty }{\underset {p_{k}:\,{primo}}{p_{k}x^{k}}}\!\!=1{+}2x{+}3x^{2}{+}5x^{3}{+}7x^{4}{+}...}$