N. N. Kalitkin, S. A. Kolganov, “Prescision approximations for Fermi–Dirak functions of integer index”, Mat. Model., 28:3 (2016), 23–32; Math. Models Comput. Simul., 8:6 (2016), 607

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Matematicheskoe modelirovanie, 2016, Volume 28, Number 3, Pages 23–32 (Mi mm3708)

This article is cited in 4 scientific papers (total in 4 papers)

Prescision approximations for Fermi–Dirak functions of integer index

N. N. Kalitkin^ab, S. A. Kolganov^ab

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

Full-text PDF (319 kB) Citations (4)

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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

$1$ ,

2

$2$ ,

3

$3$ , which provide ratio error

2 \cdot 10^{- 16}

$2\cdot10^{-16}$ with

9

$9$ free parametrs.

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

Funding agency	Grant number
Russian Foundation for Basic Research	14-01-00161_а

Received: 21.04.2015

English version:
Mathematical Models and Computer Simulations, 2016, Volume 8, Issue 6, Pages 607–614
DOI: https://doi.org/10.1134/S2070048216060090

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: N. N. Kalitkin, S. A. Kolganov, “Prescision approximations for Fermi–Dirak functions of integer index”, Mat. Model., 28:3 (2016), 23–32; Math. Models Comput. Simul., 8:6 (2016), 607–614

Citation in format AMSBIB

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\by N.~N.~Kalitkin, S.~A.~Kolganov

\paper Prescision approximations for Fermi--Dirak functions of integer index

\jour Mat. Model.

\yr 2016

\vol 28

\issue 3

\pages 23--32

\mathnet{http://mi.mathnet.ru/mm3708}

\elib{https://elibrary.ru/item.asp?id=25865435}

\transl

\jour Math. Models Comput. Simul.

\yr 2016

\vol 8

\issue 6

\pages 607--614

\crossref{https://doi.org/10.1134/S2070048216060090}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84994894976}

Linking options:

https://www.mathnet.ru/eng/mm3708

https://www.mathnet.ru/eng/mm/v28/i3/p23

This publication is cited in the following 4 articles:

N. N. Kalitkin, S. A. Kolganov, “Postroenie approksimatsii, udovletvoryayuschikh chebyshevskomu alternansu”, Preprinty IPM im. M. V. Keldysha, 2020, 091, 33 pp.
N. N. Kalitkin, S. A. Kolganov, “Correction of the precision approximations of the Fermi–Dirac functions of integer index”, Math. Models Comput. Simul., 9:5 (2017), 554–560
N. N. Kalitkin, S. A. Kolganov, “Calculation of the Fermi–Dirac functions with exponentially convergent quadratures”, Math. Models Comput. Simul., 10:4 (2018), 472–482
Kalitkin N.N. Kolganov S.A., “Quadrature Formulas With Exponential Convergence and Calculation of the Fermi-Dirac Integrals”, Dokl. Math., 95:2 (2017), 157–160

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	149
References:	86
First page:	34

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