This article is cited in 4 papers

Prescision approximations for Fermi–Dirak functions of integer index

N. N. Kalitkin^ab, S. A. Kolganov<sup>ab

a</sup> Keldysh Institute of Applied Mathematics of Rus. Acad. Sci., Moscow
^b National Research University of Electronic Technology, Zelenograd

Abstract: 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.

Keywords: Fermi–Dirak functions, precision approximations, rational approximation, linear-trigonometric grid.

Received: 21.04.2015

 English version: Mathematical Models and Computer Simulations, 2016, 8:6, 607–614

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