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[tex]\frac{1}{|x_1-x_2|} = \sum_{l=0} \frac{r_{<}^l}{r_{>}^{l+1}}P_{l}\left(cos\left(\gamma\right)\right)[/tex]

Where r< is the lesser of |x1| and |x2| and P_l are the legendre polynomials.

I have included up to 4 terms and the resultant potential isn't resembling the expected potential curve. Does anyone have any experience with such expansions, or would you recommend a different expansion (I ultimately need it to make a function integrable) ?