Journal Article10.1119/1.1934430
Integrals over the Fermi Function
30
TL;DR: In this article, a formal device for evaluating integrals over the Fermi distribution function is presented, and an expansion of the formal solution yields Sommerfeld's familiar result obtained in connection with the electron theory of metals.
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Abstract: A formal device for evaluating integrals over the Fermi distribution function is presented. An expansion of the formal solution yields Sommerfeld's familiar result obtained in connection with the electron theory of metals. In special cases, the result can be expressed in closed form. One such case, the scattering form factor for the Fermi distribution, is presented. Application of the method to other integrals is indicated.
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Citations
A note on Sommerfeld's formula for Fermi-Dirac integrals
TL;DR: Sommerfeld's formula for approximate evaluation of integrals involving the Fermi-Dirac function is derived by the Laplace transform method, and its limitations are discussed in this article.
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