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An efficient algorithm for the direct evaluation of Fermi-Dirac integrals of half orders is presented. The computational scheme consists of a modified trapezoidal rule which exactly corrects for the loss of accuracy caused by the presence of poles of the integrand. The analysis of the scheme leads to useful error bounds which indicate the quadrature 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 1014 for the usual range of values of the argument.

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