Rational Chebyshev approximations for Fermi-Dirac integrals of orders -1/2, 1/2 and 3/2

Abstract

Rational Chebyshev approximations are given for the complete Fermi-Dirac integrals of orders − 1 2 - \frac {1} {2} 1 2 \frac {1} {2} and 3 2 \frac {3} {2} . Maximal relative errors vary with the function and interval considered, but generally range down to 10 − 9 {10^{ - 9}} or less.