MECÂNICA GENERALIZADA GRACELI - QUÂNTICA QUÍMICA RELATIVISTA [211]

EQUAÇÃO DE LAPLACE COM FUNÇÕES DE GRACELI.

Em um conjunto aberto ${\textstyle U\subset {\mathbb {R}}^{n}}$ , a equação de Laplace é definida por:[1]

$\Delta f = 0$

onde, ${\textstyle \Delta }$ denota o operador de Laplace (ou, laplaciano):

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$

EQUAÇÃO GRACELI COM FATORIAL E ZETA.

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $+ [$ -COS] $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + $n!$ / [PK] $\zeta (s)$ /2 =

EQUAÇÃO GRACELI COM FATORIAL E ZETA.

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $+$ $n \choose k$ $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n]

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n \choose k$ $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n \choose k$ $B An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + $n!$ / [PK] $\zeta (s)$ /2 + SEN B / A $n!$ $\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n \choose k$ $B An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + $n!$ / [PK] $\zeta (s)$ /2

EQUAÇÃO GRACELI COM FATORIAL E ZETA.

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $+ An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + SEN $n!$ / [PK] $\zeta (s)$

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + $n!$ / [PK] $\zeta (s)$ /2 =

EQUAÇÃO GRACELI COM FATORIAL E ZETA.

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n \choose k$ $An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $n \choose k$ $B An$ $n!$ / [PK] $\zeta (s)$ [-pk] / $n!$ / [PK] $\zeta (s)$ [n] + $n!$ / [PK] $\zeta (s)$ /2 =

FUNÇÃO GRACELI.

P = PROGRESSÃO.

K = VARIÁVEL COMPLEXA.

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $\zeta (s)$ = [-1[ $n!$ ]] / f [-1[ $n!$ ]] / [u [ $n!$ / PK] $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ ] / û [ $n!$ / PK $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ / [ $n!$ ]- x dx

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ $\zeta (s)$ = f [u [ $n!$ / PK] $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ ] / û [ $n!$ / PK $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ /[ $n!$ ]- x dx

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ f [u [ $n!$ / PK] $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ ] / û [ $n!$ / PK $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ - x dx [-1]=

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ f [u [ $n!$ / PK] $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ ] / û [ $n!$ / PK $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ - x [+1] dx = 0

\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }

f [u [

n!

/ PK]

\zeta (s)

\mathrm {e^{i2\pi \phi }}

] / û [

n!

/ PK

\zeta (s)

\mathrm {e^{i2\pi \phi }}

- x dx

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ COS [ $n!$ / PK] $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ [+,-] SIN [ $n!$ /PK] $\zeta (s)$ $\mathrm {e^{i2\pi \phi }}$ =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ COS [ $n!$ /PK] $\Gamma (z)$ $\mathrm {e^{i2\pi \phi }}$ [+,-] SIN [ $n!$ / PK] $\Gamma (z)$ $\mathrm {e^{i2\pi \phi }}$ =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ COS [ $n!$ /PK] $\psi _{n}(z)$ $\mathrm {e^{i2\pi \phi }}$ [+,-] SIN [ $n!$ / PK] $\psi _{n}(z)$ $\mathrm {e^{i2\pi \phi }}$ =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ COS [ $n!$ / PK] $\operatorname {Li} _{s}(z)$ $\mathrm {e^{i2\pi \phi }}$ [+,-] SIN [ $n!$ / PK $\operatorname {Li} _{s}(z)$ $\mathrm {e^{i2\pi \phi }}$ =

$\Delta f := \sum_{i=1}^n \frac{\partial^2 f}{\partial x_i^2 }$ COS [ $n!$ /PK] $E_{n}$ $\mathrm {e^{i2\pi \phi }}$ [+,-] SIN [ $n!$ /PK] $E_{n}$ $\mathrm {e^{i2\pi \phi }}$ =

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