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Zbl 0758.65012
Paszkowski, S.
Evaluation of the Fermi-Dirac integral of half-integer order. (English)
[J] Zastosow. Mat. 21, No.2, 289-301 (1991). ISSN 0044-1899

The author computes $F\sb \mu$ for half-integer $\mu$ and for $z\le 2$, where $F\sb \mu$ is defined by the integral $F\sb \mu(x)=\int\sp \infty\sb 0(1+e\sp{x-2})\sp{-1}x\sp \mu dx$, $\mu>-1$. He also shows that it is possible to evaluate $F\sb \mu(z)$ for half-integer $\mu$ and for sufficiently greater $z$, say for $z\ge 2$, with accuracy only a bit worse than that which is guaranteed by the arithmetic in use. The same methods could be used to evaluate some linear combinations of $F\sb \mu$ important in certain physical applications.\par Since there are well-known difficulties associated with rational interpolation and approximation, such as nonexistence of an interpolant, rather complicated characterization of the best approximation is required. This phenomenon does not occur in the cases considered here.
[R.S.Dahiya (Ames)]

MSC 2000:: *65D20 Computation of special functions
41A20 Approximation by rational functions
30B70 Continued fractions (function-theoretic results)
33B20 Incomplete beta and gamma functions

Keywords: Fermi-Dirac integral; continued fraction; series expansion; convergence acceleration; best rational approximation

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