CDROM/APJS/V105/P407    Fermi-Dirac Integrals and Derivatives (Miralles+ 1996)
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Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for
Arbitrary Degeneracy and Relativity
      Juan Antonio Miralles and Kenneth A. Van Riper
      <1996, ApJS, 105, 407>
      =1996ApJS..105..407M
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Abstract:
     The equation of state of an ideal Fermi gas is expressed in terms
  of Fermi-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 tables and a FORTRAN subroutine for numerical
  evaluation in the integrals and derivatives when a limit does not
  apply.  The functions can be evaluated to better than 1% accuracy for
  any temperature and density using these methods.

Keywords: dense matter -- equation of state -- relativity --
          stars: neutron

Description:
     Three tables of integrals accompany this paper.  The file
  fdints.tab contains the Fermi-Dirac integrals and the Fermi
  integrals.  The file dfdints.tab contains the derivatives of the
  Fermi-Dirac and of the Fermi integrals.  The Bessel functions are
  found in bessel.tab.  The file fermi7h.tab contains the Fermi
  integrals of order 7/2.  These tables are read by FORTRAN subroutine
  calcdfi, which is also provided along with the tables; the exact
  format of the tables can be found by examining the relevant READ
  statements in the subroutine.  The functions and the derivatives are
  maintained as separate files to facilitate implementations where
  only the function values are required; subroutine calcfi, also
  supplied, is a variant of calcdfi with the derivatives stripped out.
     Subroutine calcdfi reads the data from the binary (or
  unformatted) files fdints.unf (which contains the Bessel data) and
  dfdints.unf if they both exist; if they do not exist, the formatted
  files fdints.tab, ... are read, and the logarithm of the data are
  written to binary files.  The binary files are preferred because the
  formatted files are 5 times as large and take 35 times longer to
  load.  All data is held in memory as (natural) logarithms.
     Note: See the author-supplied README file for details on
  compiling and installing the FORTRAN programs.

File Summary:
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File Name    Lrecl    Records   Explanations
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bessel.tab      40         59   Bessel functions
dfdints.tab    112       1088   Derivatives of Fermi-Dirac and Fermi integrals
fermi7h.tab     24        101   Fermi integrals of order 7/2
fdints.tab     104       1088   Fermi-Dirac and Fermi integrals
Makefile        73         33   Makefile for FORTRAN programs
README          72        104   Author-supplied description
besscheb.f      75        240   Author-supplied FORTRAN source code
calcdfi.f       73        740   Author-supplied FORTRAN source code
calcfi.f        73        511   Author-supplied FORTRAN source code
fdeos.f         72        174   Author-supplied FORTRAN source code
fdstitch.f      72        222   Author-supplied FORTRAN source code
polyint.f       71         74   Author-supplied FORTRAN source code
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(End)                                               Lee Brotzman [ADS] 13-Aug-96