THE ACCURATE NUMERICAL EVALUATION OF HALF-ORDER FERMI-DIRAC INTEGRALS

An efficient algorithm for the direct evaluation of Fermi-Dirac integr als of half orders is presented. The computational scheme consists of a modified trapezoidal rule which exactly corrects for the loss of acc uracy caused by the presence of poles of the integrand. The analysis o f the scheme leads to useful error bounds which indicate the quadratur e scheme to be rapidly convergent. As much as 16 steps of trapezoidal summation along with at most 9 steps of pole correction can provide an accuracy of one part in 10(14) for the usual range of values of the a rgument.