\frac{1}{\Delta} = \frac{1}{r} (1 + 2 \frac{a}{r} \cos \varphi \cos (\alpha -\lambda) + (\frac{a}{r})^2)^{-1/2}

Or (1+x)^{-1/2} = 1 - \frac{x}{2} + \frac{3}{8} x^2 + ...

On en déduit que:

\frac{1}{\Delta} = \frac{1}{r} (1 - \cos \varphi \cos (\alpha -\lambda) (\frac{a}{r}) + (\frac{3}{2} \cos^2 \varphi \cos^2(\alpha -\lambda) - \frac{1}{2})(\frac{a}{r})^2)