Analytical Expansion and Numerical Approximation of the Fermi-Dirac Integrals {\cal F}j(x) of Order j=−1/2 and j=1/2

  • Authors:

  • Frank G. Lether

  • Affiliations:

  • Mathematics Department, Boyd Graduate Research Center, University of Georgia, Athens, Georgia 30602-7403/ fglether@math.uga.edu

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2000

Quantified Score

Hi-index 0.01

Visualization

Abstract

This paper uses properties of the Weyl semiintegral and semiderivative, along with Oldham's representation of the Randles–Sevcik function from electrochemistry, to derive infinite series expansions for the Fermi–Dirac integrals {\cal F}j(x), −∞j=−1/2, 1/2. The practical use of these expansions for the numerical approximation of {\cal F}−1/2(x) and {\cal F}1/2(x) over finite intervals is investigated and an extension of these results to the higher order cases j=3/2, 5/2, 7/2 is outlined.