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Evaluation of Fermi-Dirac integral. (English) Zbl 0673.65010
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.]

The author considers general methods for the Fermi-Dirac integral F μ (z)= 0 z x μ (1+exp(x-z)) -1 dx, μ>-1 and distinguishes three cases: (i) μ=1,2,···,z0 and the non- polynomial part of F μ (z) is expanded, after a suitable variable transformation, into Chebyshev series; (ii)μ=-,,···,z0 is sufficiently small and F μ (z) is expanded in powers of x=1-(1+e z ) 1/2 ; (iii) μ=-,,···,zu 2 , with a sufficiently large u and F μ (z) is expanded at first into a series containing the functions Erfi and Erfc and, after that, into Chebyshev series with the variable u/z.

Reviewer: R.S.Dahiya
MSC:
65D20Computation of special functions, construction of tables
33E99Other special functions