EQUAÇÕES GRACELI [7]

${n \choose k}={n! \over k!(n-k)!}.$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

$\ln(n!)=\sum _{{k=1}}^{n}{\ln(k)}$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

$\ln(n!)\approx n\ln(n)-n+{\frac {\ln(n)}{2}}+{\frac {\ln(2\pi )}{2}}.$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

$\Gamma \left(n+{1 \over 2}\right)={\sqrt \pi }{(2n-1)!! \over 2^{n}}$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

$(n-1)!={\frac {n!}{n}}$ / [PK] $\psi ^{*}$ $\psi$ ]

$z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

$S=\sum _{{n\geq 1}}{\frac {1}{n^{\alpha }}}$ . $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi ^{*}$ $\psi$ ]

$S=\sum _{{n\geq 1}}{\frac {1}{n^{\alpha }}}$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

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

$\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

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

$\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi ^{*}$ $\psi$ ]

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi ^{*}$ $\psi$ ]

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi ^{*}$ $\psi$ ].

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EQUAÇÕES GRACELI [7]

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