6533b823fe1ef96bd127f6f9
RESEARCH PRODUCT
Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for Arbitrary Degeneracy and Relativity
Kenneth A. Van RiperJuan A. Mirallessubject
PhysicsEquation of stateIdeal (set theory)Mathematical modelAstrophysics (astro-ph)FOS: Physical sciencesAstronomy and AstrophysicsAstrophysicssymbols.namesakeTheory of relativitySpace and Planetary SciencesymbolsFermi–Dirac statisticsLimit (mathematics)Fermi gasDegeneracy (mathematics)Mathematical physicsdescription
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 of 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1996-08-01 | The Astrophysical Journal Supplement Series |