Analytical approximation of the Fermi-Dirac integrals of half-integer and integer orders
- Authors: Koroleva O.N.1,2, Mazhukin A.V.1,2, Mazhukin V.I.1,2, Breslavskiy P.V.1
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Affiliations:
- Keldysh Institute of Applied Mathematics
- National Research Nuclear University MEPhI
- Issue: Vol 9, No 3 (2017)
- Pages: 383-389
- Section: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/201777
- DOI: https://doi.org/10.1134/S2070048217030073
- ID: 201777
Cite item
Abstract
We have obtained continuous analytical expressions approximating the Fermi-Dirac (F-D) integrals of orders j = −1/2, 1/2, 1, 3/2, 2, 5/2, 3, and 7/2 in a convenient form for calculation with reasonable accuracy (1–4)% in a wide degeneration range in this paper. An approach based on the least squares method for approximation was used. The demands for the approximation of integrals, the range of variation of order j, and the definitional domain are considered in terms of the use of F-D integrals to determine the properties of metals and semiconductors.
About the authors
O. N. Koroleva
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Email: vim@modhef.ru
Russian Federation, Moscow; Moscow
A. V. Mazhukin
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Email: vim@modhef.ru
Russian Federation, Moscow; Moscow
V. I. Mazhukin
Keldysh Institute of Applied Mathematics; National Research Nuclear University MEPhI
Author for correspondence.
Email: vim@modhef.ru
Russian Federation, Moscow; Moscow
P. V. Breslavskiy
Keldysh Institute of Applied Mathematics
Email: vim@modhef.ru
Russian Federation, Moscow