Edit: Figured it out!
[itex] ∑ A_lR^lP_l(cos\theta) = -E_0Rcos\theta + ∑ \frac{B_l}{R^{l+1}}P_l(cos\theta) [/itex]
Goes to,
[itex] A_lR^l = \frac{B_l}{R^{l+1}} [/itex]
for l = l' not equal to 1
[itex] ∑ A_lR^lP_l(cos\theta) = -E_0Rcos\theta + ∑ \frac{B_l}{R^{l+1}}P_l(cos\theta) [/itex]
Goes to,
[itex] A_lR^l = \frac{B_l}{R^{l+1}} [/itex]
for l = l' not equal to 1