Fermi-Dirac integrals in terms of Zeta Functions

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.