EQUAÇÕES GRACELI [8]

janeiro 21, 2023

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

COS $\sum _{k=1}^{n}k^{m}z^{k}=\left(z{\frac {d}{dz}}\right)^{m}{\frac {1-z^{n+1}}{1-z}}$ $\sum _{k=0}^{m}k^{n-1}={\frac {B_{n}(m+1)-B_{n}}{n}}$ $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi _{n}(z)$ $\psi ^{*}$ $\psi$ ]

COS $\sum _{k=1}^{n}k^{m}z^{k}=\left(z{\frac {d}{dz}}\right)^{m}{\frac {1-z^{n+1}}{1-z}}$ $\sum _{k=0}^{m}k^{n-1}={\frac {B_{n}(m+1)-B_{n}}{n}}$ $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi _{n}(z)$ $\psi ^{*}$ $\psi$ ].

$COS$ $\sum _{k=1}^{n}k^{m}z^{k}=\left(z{\frac {d}{dz}}\right)^{m}{\frac {1-z^{n+1}}{1-z}}$ $\sum _{k=0}^{m}k^{n-1}={\frac {B_{n}(m+1)-B_{n}}{n}}$ . $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi _{n}(z)$ $\psi ^{*}$ $\psi$ ]

$COS$ $\sum _{k=1}^{n}k^{m}z^{k}=\left(z{\frac {d}{dz}}\right)^{m}{\frac {1-z^{n+1}}{1-z}}$ $\sum _{k=0}^{m}k^{n-1}={\frac {B_{n}(m+1)-B_{n}}{n}}$ . $z!=\Gamma (z+1)=\int _{{0}}^{{\infty }}t^{z}e^{{-t}}\,dt$ [PK] $\psi _{n}(z)$ $\psi ^{*}$ $\psi$ ].

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

$\sum _{k=0}^{\infty }{\frac {z^{k}}{k!}}=e^{z}$ $\psi _{n}(z)$ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi _{n}(z)$ $\psi ^{*}$ $\psi$ ]

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

$\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ . $(n-1)!={\frac {n!}{n}}$ / [PK] $\psi _{n}(z)$ $\sum _{k=0}^{\infty }{\frac {z^{k}}{k!}}=e^{z}$

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

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ $(n-1)!={\frac {n!}{n}}$ $n \choose k$ / [PK] $\sum _{k=0}^{\infty }k^{n}{\frac {z^{k}}{k!}}=z{\frac {d}{dz}}\sum _{k=0}^{\infty }k^{n-1}{\frac {z^{k}}{k!}}\,\!=e^{z}T_{n}(z)$

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ $n \choose k$ [PK] $\sum _{k=0}^{\infty }k^{n}{\frac {z^{k}}{k!}}=z{\frac {d}{dz}}\sum _{k=0}^{\infty }k^{n-1}{\frac {z^{k}}{k!}}\,\!=e^{z}T_{n}(z)$ $\sum _{k=0}^{\infty }{\frac {(-1)^{k}z^{2k+1}}{(2k+1)!}}=\mathrm {sen} \,z$

$\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ . $(n-1)!={\frac {n!}{n}}$ / [PK] $\sum _{k=0}^{\infty }{\frac {(-1)^{k}z^{2k+1}}{(2k+1)!}}=\mathrm {sen} \,z$

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

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EQUAÇÕES GRACELI [8]

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