Über das asymptotische Verhalten des Fermi–Dirac-Integrals

  • Hans-Joachim Schell

    Technische Universität Chemnitz, Germany

Abstract

New asymptotic expansions of the Fermi-Dirac integral Fp1(x)F_{p^–1}(x) are derived in the case that both xx and pp tend to infinity: a) for pxp \sim x, b) for p=ax,0<a<2p = ax, 0 < a < 2. A new asymptotic approximation is given for p,p=o(p2x)p \to \infty, \sqrt p = o(p - 2x). The values calculated with these formulas are for several pairs (x,p)(x, p) compared with the exact values.

Cite this article

Hans-Joachim Schell, Über das asymptotische Verhalten des Fermi–Dirac-Integrals. Z. Anal. Anwend. 6 (1987), no. 5, pp. 421–438

DOI 10.4171/ZAA/261