Über das asymptotische Verhalten des Fermi–Dirac-Integrals

Abstract

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