ACCURATE EVALUATION OF FERMI-DIRAC INTEGRALS AND THEIR DERIVATIVES FOR ARBITRARY DEGENERACY AND RELATIVITY

The equation of state of an ideal Fermi gas is expressed in terms of F ermi-Dirac integrals. We give formulae for evaluation the Fermi-Dirac integrals of orders 1/2, 3/2, and 5/2 and their derivatives in various limits of non- and extreme degeneracy and relativity. We provide tabl es and a FORTRAN subroutine for numerical evaluation of the integrals and derivatives when a limit does not apply. The functions can be eval uated to better than 1% accuracy for any temperature and density using these methods.