Multipole

#Physics
Complex charge distributions can be approximated as a sum of different poles from far away enough
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$\displaystyle V(\vec{r})=k\sum_{n = 0}^{\infty} \frac{1}{r^{(n+1)}}\int (r')^{n}P_{n}(\cos \alpha)\rho (\vec{r}') , \mathrm{d}\tau'$

Voltage of a charge density
$\displaystyle k$ is the Coloumb constant
$\displaystyle r$ is the position vector magnitude
$\displaystyle r'$ is the source vector magnitude
$\displaystyle P_{n}$ is the Legendre Polynomial
$\displaystyle \alpha$ is the angle between the position vector and source vector
$\displaystyle \tau'$ is the volume element