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The monikers "FermiDirac", "generalized FermiDirac", and "Fermi" function haven't received uniform usage in the literature. I'll use the term "FermiDirac" function for the two parameter integral: \begin{equation} F_{k}(\eta,\theta) = \int\limits_{0}^{\infty} \ {x^{k} \ (1 + 0.5 \ \theta \ x)^{1/2} \over \exp(x  \eta) + 1} \ dx \label{eq1} \tag{1} \end{equation} where $k$ is the order of the function, $\theta = k_B T / (mc^2)$ is the relativity parameter, and $\eta = \mu/(k_B T)$ is the normalized chemical potential energy $\mu$, which is sometimes called the degeneracy parameter. I'll reserve the term "Fermi" function as a special case, $\theta=0$, of the FermiDirac function: \begin{equation} F_{k}(\eta) = \int\limits_{0}^{\infty} \ {x^{k} \ \over \exp(x  \eta) + 1} \ dx \label{eq2} \tag{2} \end{equation} The Fermi function can be obtained from some remarkable rational function fits from H.M. Antia (ApJS 84, 101, 1993 and private communication 1995). These rational function approximations are compared to the exact answers given by the FermiDirac quadratures in the code contained in this bzip2 tarball fermi.tbz. The FermiDirac function may be solved by two methods. The first uses an exactasyoulike direct simpson integration on nested grids in tandem with some integral transformations. I've called this Cloutman's method (ApJS 71, 677, 1989). Some of my trivial additions were to generalize from the Fermi functions to the FermiDirac functions in the code contained in this bzip2 tarball fermi_dirac.tbz. The second method solves the FermiDirac functions by an asexactasyoulike quadrature method. You may be very pleasantly suprised at how efficiently it runs for the accuracy achieved. The original idea and code comes from Josep Aparicio (ApJS 117, 627, 1998). My trivial contributions have been to add the first and second derivatives, and gather the various quadrature accuracies under one roof in the code contained in this bzip2 tarball fermi_dirac_with_derivatives.tbz. If you want to see how the FermiDirac functions are used in a bare knuckle stellar equation of state, take a look at the Timmes eos routine. 


Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer coauthorship as appropriate. 
