Complete Fermi-Dirac-integral

Arguments:

• j
• x

Formula: ${F_j(x) = \frac{1}{\Gamma(j+1)} \int_0^{\infty}{\frac{t^j}{\exp(t-x)+1}dt}}$

Implementation: Using the polylogarithm

Approximation of the complete Fermi-Dirac-integral for j = 1/2

Checked for a relative tolerance of 3% in the range x = -100:0.1:100

Speed: 100 times faster than the polylog version

Source: J. S. Blakemore: Approximations for Fermi-Dirac Integrals. Solid-State Electronics, 25(11):1067-1076, 1982.