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The terms "FermiDirac", "generalized FermiDirac", and "Fermi" function haven't received uniform usage in the literature. I'll use "FermiDirac" 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 use "Fermi" function as the $\theta=0$ special case 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 functions can be obtained from some remarkable rational function approximations. The FermiDirac function are solved by two methods. The first uses simpson integration on nested grids in tandem with integral transformations. The second method uses quadrature summations (Also see this article). The answers these methods produce are compared in fermi_dirac.tbz. My contributions to fermi_dirac.tbz include adding the first and second partial derivatives to the quadrature method, and gathering the various quadrature accuracies under one roof. To see how these FermiDirac functions are used in a bare knuckle stellar equation of state, peek at the Timmes eos instrument. 


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