Geodesic
Prescision approximations for Fermi--Dirak functions of integer index
Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 23-32

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Fermi–Dirak functions of integer index are widely used in problems of electronic transport in dense substances. Polynomial approximations are constructed for its quick computation. A simple algorithm is built for finding the coefficients of these approximations based on interpolation with a special linear-trigonometric grid nodes. Represented that this grid provides results close to optimal. Such coefficients are founded for functions of index $1$, $2$, $3$, which provide ratio error $2\cdot10^{-16}$ with $9$ free parametrs.
Mots-clés : Fermi–Dirak functions
Keywords: precision approximations, rational approximation, linear-trigonometric grid. 
@article{MM_2016_28_3_a1,
     author = {N. N. Kalitkin and S. A. Kolganov},
     title = {Prescision approximations for {Fermi--Dirak} functions of integer index},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {23--32},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_3_a1/}
}
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N. N. Kalitkin; S. A. Kolganov. Prescision approximations for Fermi--Dirak functions of integer index. Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 23-32. http://geodesic.mathdoc.fr/item/MM_2016_28_3_a1/