Analytical approximation of the Fermi--Dirac integrals of half-integer and integer orders

O. N. Koroleva; A. V. Mazhukin; V. I. Mazhukin; P. V. Breslavskiy

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Analytical approximation of the Fermi--Dirac integrals of half-integer and integer orders

O. N. Koroleva ; A. V. Mazhukin ; V. I. Mazhukin ; P. V. Breslavskiy

Matematičeskoe modelirovanie, Tome 28 (2016) no. 11, pp. 55-63

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Résumé

We obtain continuous analytical expressions approximating the Fermi–Dirac integrals of orders $j=-1/2, 1/2, 1, 3/2, 2, 5/2, 3, 7/2$ in a convenient form for calculation with reasonable accuracy $(1\div4)\%$ in a wide range of the degeneration in this paper. An approach based on the least square method for approximation was used. The demands to the approximation of integrals, to the range of variation of order j and to the definitional domain are considered in terms of the use of Fermi–Dirac integrals to determine the properties of metals and semiconductors.

Keywords: Fermi–Dirac integrals, analytical approximation.

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     author = {O. N. Koroleva and A. V. Mazhukin and V. I. Mazhukin and P. V. Breslavskiy},
     title = {Analytical approximation of the {Fermi--Dirac} integrals of half-integer and integer orders},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {55--63},
     publisher = {mathdoc},
     volume = {28},
     number = {11},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_11_a3/}
}

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O. N. Koroleva; A. V. Mazhukin; V. I. Mazhukin; P. V. Breslavskiy. Analytical approximation of the Fermi--Dirac integrals of half-integer and integer orders. Matematičeskoe modelirovanie, Tome 28 (2016) no. 11, pp. 55-63. http://geodesic.mathdoc.fr/item/MM_2016_28_11_a3/