High Quality Content by WIKIPEDIA articles! A Sommerfeld expansion is an approximation method developed by Arnold Sommerfeld for a certain class of integrals which are common in condensed matter and statistical physics. Physically, the integrals represent statistical averages using the Fermi–Dirac distribution. When is a large quantity, it can be shown that int_{-infty}^infty frac{H(varepsilon)}{e^{beta(varepsilon - mu)} + 1},mathrm{d}varepsilon = int_{-infty}^mu H(varepsilon),mathrm{d}varepsilon + frac{pi^2}{6}left(frac{1}{beta}right)^2H^prime(mu) + mathrm{O} left(frac{1}{betamu}right)^4 where H^prime(mu) is used to denote the derivative of H(varepsilon) evaluated at varepsilon = mu and we have used Big-O notation to describe the approximation's limiting behaviour.

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