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Manuscript Title: Generalized Fermi-Dirac functions and derivatives: properties and evaluation.
Authors: Z. Gong, L. Zejda, W. Dappen, J.M. Aparicio
Program title: GFD_D3
Catalogue identifier: ADNX_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 136(2001)294
Programming language: Fortran.
Computer: Sun E4500/E5500, Compaq DEC Alpha, SGI Origin 2000, HP Convex Exemplar, Cray SV1-1A/16-8, AMD K6 PC, IBM SP2.
Operating system: Solaris 5.6, Linux (Red Hat 5.2), IRIX 64, SPP-UX 5.3, Unicos, Microsoft Windows 98 (2nd edn.), AIX 4.2.
Keywords: Fermi-Dirac functions, Equation of state, Electron gas, Numeric method, Astrophysics plasma, Stellar evolution, General purpose.
Classification: 4.7.

Nature of problem:
Provide numerical method to evaluate generalized Fermi-Dirac functions and their derivatives with respect to eta and beta up to third order. The results are important for a highly accurate calculation of thermodynamic quantities of an electron gas with partial degeneracy and relatively high temperatures with very high order of accuracy.

Solution method:
Following the scheme proposed by Aparicio [1], the generalized Fermi-Dirac integration is split into four optimized regions. Gauss-Legendre quadrature is used in the first three pieces, and Gauss-Laguerre quadrature in the last part when the e^-x term in the integrand dominates. Different break points are individually chosen for each eta derivative.

Running time:
Less than 1 ms for each data point on a DEC Alpha station with a 533 MHz CPU in double precision.