  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.
