I have

$\displaystyle V(x)=G\int_V{\frac{\rho(\bold{x}^{'})d\bold{x}^{'} }{|\bold{x}-\bold{x}^{'}|}$

how do I verify that

$\displaystyle \nabla^{2}V=-4\pi G \rho $

?

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- Nov 8th 2010, 10:12 AMJason BournePoisson's equation verification
I have

$\displaystyle V(x)=G\int_V{\frac{\rho(\bold{x}^{'})d\bold{x}^{'} }{|\bold{x}-\bold{x}^{'}|}$

how do I verify that

$\displaystyle \nabla^{2}V=-4\pi G \rho $

?