In Wikipedia's article on Fermi Gases, they have an equation for the chemical potential; http://en.wikipedia.org/wiki/Fermi_gas .

I don't understand how they get the third term, particularly the 1/80 factor. I've often seen this equation expressed just to the tau^2 term, and I understand how to get the 1/12 factor (from a binomial expansion of
$$ 1 + \frac{1}{8} \left(\tau\frac{\pi}{E}\right)^{-2/3}. $$

However, I've tried continuing the binomial expansion and cannot figure out why the factor is 1/80.