Evaluation of Some Fermi-Dirac Integrals
- 1 February 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (2), 477-482
- https://doi.org/10.1063/1.1665160
Abstract
The evaluation of Fermi‐Dirac integrals is discussed for cases in which the Sommerfeld method fails. Such cases occur when the integrand has a singularity at the Fermi surface and when the integrand is a rapidly oscillating function. As examples, the first‐order exchange integral for electrons and the free‐energy integral of the noninteracting electron gas in a magnetic field are evaluated. The method uses a contour‐integral representation of the Fermi function (previously mentioned by Dingle), supplemented by Mittag‐Leffler type expansions.Keywords
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