Problem $3\mathrm{.}20$ Suppose the potential $V_0()$ at the surface of a sphere is specified, and there is no charge inside or outside the sphere. Show that the charge density on the sphere is given by

$()=\frac{lo{n}_0}{2R}{\displaystyle \underset{l=0}{\overset{}{}}}(2l+1{)}^2{C}_l{P}_l(cos),$

where

$C_l={\displaystyle \underset{0}{\overset{}{}}}{V}_0()P_l(cos)sind$

Can you please help me solve this with methods like laplace, poisson