Complete asymptotic expansions of the Fermi-Dirac integrals F[sub p](η)=1/Γ(p+1)∫[sub 0][sup ∞][ε[sup p]/(1+e[sup ε-η])]dε.

The complete asymptotic expansions, that is to say expansions which include any exponentially small terms lying beyond all orders of the asymptotic power series, are calculated for the Fermi-Dirac integrals. We present two methods to accomplish this, the first in the complex plane utilizing Mellin transforms and Hankel's representation of the gamma function, and the second on the real line using the known asymptotic expansions of the confluent hypergeometric functions. The complete expansions of F[sub p](η) are then used to investigate the effect that these traditionally neglected exponentially small terms have on physical systems. It is shown that for a 2 dimensional nonrelativistic ideal Fermi gas, the subdominant exponentially small series becomes dominant. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]