FUNÇÕES ZETA COM FATORIAL E PROGRESSÕES.

FUNÇÕES COM FATORIAL E PROGRESSÕES.

$\Gamma (n+1)=n!$ ou $\Gamma (n)=(n-1)!$ / $n!$ / [PK] $\zeta (s)$ [n]

$\Gamma (n+1)=n!$ ou $\Gamma (n)=(n-1)!$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\Gamma (n+1)=n!$ ou $\Gamma (n)=(n-1)!$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$L(s,\chi )=\sum _{n=1}^{\infty }{\frac {\chi (n)}{n^{s}}}.$ / $n!$ / [PK] $\zeta (s)$ [n]

$L(s,\chi )=\sum _{n=1}^{\infty }{\frac {\chi (n)}{n^{s}}}.$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$L(s,\chi )=\sum _{n=1}^{\infty }{\frac {\chi (n)}{n^{s}}}.$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\vartheta (z;\tau )=\sum _{n=-\infty }^{\infty }\exp(\pi in^{2}\tau +2\pi inz)=1+2\sum _{n=1}^{\infty }\left(e^{\pi i\tau }\right)^{n^{2}}\cos(2\pi nz).$ / $n!$ / [PK] $\zeta (s)$ [n] $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\vartheta (z;\tau )=\sum _{n=-\infty }^{\infty }\exp(\pi in^{2}\tau +2\pi inz)=1+2\sum _{n=1}^{\infty }\left(e^{\pi i\tau }\right)^{n^{2}}\cos(2\pi nz).$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$f(a,b)=\sum _{n=-\infty }^{\infty }a^{n(n+1)/2}\;b^{n(n-1)/2}$ / $n!$ / [PK] $\zeta (s)$ [n]

$f(a,b)=\sum _{n=-\infty }^{\infty }a^{n(n+1)/2}\;b^{n(n-1)/2}$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$f(a,b)=\sum _{n=-\infty }^{\infty }a^{n(n+1)/2}\;b^{n(n-1)/2}$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\eta (s)=\left(1-2^{1-s}\right)\zeta (s)$ / $n!$ / [PK] $\zeta (s)$ [n]

$\eta (s)=\left(1-2^{1-s}\right)\zeta (s)$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\eta (s)=\left(1-2^{1-s}\right)\zeta (s)$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

FUNÇÃO ZETA COM FATORIAL E PROGRESSÕES.

$\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta (s)=\sum _{k=1}^{\infty }f(k)^{s}$ / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta _{K}(s)=\sum _{I\subseteq O_{K}}(N_{K/\mathbb {Q} }(I))^{-s}$ / $n!$ / [PK] $\zeta (s)$ [n]

$Z_{V,Q}(s)$ / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta _{V,p}\left(p^{-s}\right).$ / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta (s,q)=\sum _{k=0}^{\infty }(k+q)^{-s}.$ / $n!$ / [PK] $\zeta (s)$ [n]

FUNÇÃO ZETA COM FATORIAL E PROGRESSÕES.

$\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta (s)=\sum _{k=1}^{\infty }f(k)^{s}$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta _{K}(s)=\sum _{I\subseteq O_{K}}(N_{K/\mathbb {Q} }(I))^{-s}$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$Z_{V,Q}(s)$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta _{V,p}\left(p^{-s}\right).$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\zeta (s,q)=\sum _{k=0}^{\infty }(k+q)^{-s}.$ $[$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

FUNÇÃO ZETA COM FATORIAL E PROGRESSÕES.

$\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\zeta (s)=\sum _{k=1}^{\infty }f(k)^{s}$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\zeta _{K}(s)=\sum _{I\subseteq O_{K}}(N_{K/\mathbb {Q} }(I))^{-s}$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$Z_{V,Q}(s)$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\zeta _{V,p}\left(p^{-s}\right).$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\zeta (s,q)=\sum _{k=0}^{\infty }(k+q)^{-s}.$ $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

EQUAÇÃO GRACELI COM FATORIAL E ZETA.

$n!$ / [PK] $\zeta (s)$ $d^{k}y \over dx^{k}$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

[-COS] A $n!$ / [PK] $\zeta (s)$ $d^{k}y \over dx^{k}$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + $n!$ / [PK] $\zeta (s)$ /2 =

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FUNÇÕES ZETA COM FATORIAL E PROGRESSÕES.

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