Algorithm 745: computation of the complete and incomplete Fermi-Dirac integral

ABSTRACT

Portable Fortran subroutines computing the Fermi-Dirac integral Fjx and the incomplete Fermi-Dirac integral Fjx,b are presented. For the first time a set of series expansions is implemented allowing these special functions to be evaluated efficiently within a prescribed accuracy for real jand x.

REFERENCES

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INDEX TERMS

Primary Classification:
  J. Computer Applications

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms

Keywords:
Euler transformation, Fermi-Dirac integral, Levin's u transform, Riemann's zeta function, asymptotic expansions, confluent hypergeometric functions, convergence acceleration, e[k] transforms, epsilon algorithm, incomplete Fermi-Dirac integral, incomplete gamma function