Complete asymptotic expansions of the Fermi-Dirac integrals F-p(eta)=1/Gamma(p+1)integral(infinity)(0)[epsilon(p)/(1+e(epsilon-eta))]d epsilon

The complete asymptotic expansions, that is to say expansions which include any exponentially small terms lying beyond all orders of the asymptotic po wer series, are calculated for the Fermi-Dirac integrals. We present two me thods to accomplish this, the first in the complex plane utilizing Mellin t ransforms and Hankel's representation of the gamma function, and the second on the real line using the known asymptotic expansions of the confluent hy pergeometric functions. The complete expansions of F-p(eta) are then used t o investigate the effect that these traditionally neglected exponentially s mall terms have on physical systems. It is shown that for a 2 dimensional n onrelativistic ideal Fermi gas, the subdominant exponentially small series becomes dominant. (C) 2001 American Institute of Physics.