Uniform asymptotic approximation of Fermi—Dirac integrals

摘要

The Fermi–Dirac integral Fq(x)=1Γ(q+1)∫0∞tq1+et−xdt, q>−1, is considered for large positive values of x and q. The results are obtained from a contour integral in the complex plane. The approximation contains a finite sum of simple terms, an incomplete gamma function and an infinite asymptotic series. As follows from earlier results, the incomplete gamma function can be approximated in terms of an error function.