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Zbl 0673.65010
Paszkowski, S.
Evaluation of Fermi-Dirac integral. (English)
[A] Nonlinear numerical methods and rational approximation, Proc. Conf., Antwerp/Belgium 1987, Math. Appl., D. Reidel Publ. Co. 43, 435-444 (1988).

[For the entire collection see Zbl 0658.00009.] \par The author considers general methods for the Fermi-Dirac integral $F\sb{\mu}(z)=\int\sp{z}\sb{0}x\sp{\mu}(1+\exp (x-z))\sp{-1}dx,$ $\mu >- 1$ and distinguishes three cases: (i) $\mu =1,2,...,z\ge 0$ and the non- polynomial part of $F\sb{\mu}(z)$ is expanded, after a suitable variable transformation, into Chebyshev series; $(ii)\quad \mu =-,,...,z\ge 0$ is sufficiently small and $F\sb{\mu}(z)$ is expanded in powers of $x=1- (1+e\sp z)\sp{1/2};$ (iii) $\mu =-,,...,z\ge u\sp 2,$ with a sufficiently large u and $F\sb{\mu}(z)$ is expanded at first into a series containing the functions Erfi and Erfc and, after that, into Chebyshev series with the variable u/$\sqrt{z}$.
[R.S.Dahiya]

MSC 2000:: *65D20 Computation of special functions
33E99 Special functions

Keywords: Fermi-Dirac integral; Chebyshev series

Citations: Zbl 0658.00009

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