Fermi-Dirac integrals in terms of Zeta Functions

2009/09/20 by Michael Morales, Morales, Michael
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.0909.3653

arxiv created 2011/05/06 · arxiv updated 2011/05/09

Abstract

This paper shows the Fermi-Dirac Integrals expressed in terms of Riemann and Hurwitz Zeta functions. This is done by defining an auxiliar function that permits rewrite the Fermi-Dirac integral in terms of simpler and known integrals resulting in the Zeta functions mentioned. The approach used here evades the use of iterative methods for the integrals and presents a generalization in a refereed interval, one that complements Sommerfeld lemma.

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