Computation of the integral Fermi-Dirac function
Matematičeskoe modelirovanie, Tome 24 (2012) no. 2, pp. 129-138.

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The Fermi-Dirac functions appear in many areas of physics. The problem of their computation has been studied for a long time. In high energy physics it is also required to compute more complex special functions that use Fermi-Dirac functions. A numerical method is suggested to allow precise computation of one of such functions which is used to calculate the exchange correction to electron energy for arbitrary temperature.
Keywords: Fermi-Dirac function, high-precision.
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R. Golovanov; K. I. Lutskiy. Computation of the integral Fermi-Dirac function. Matematičeskoe modelirovanie, Tome 24 (2012) no. 2, pp. 129-138. http://geodesic.mathdoc.fr/item/MM_2012_24_2_a8/

[1] Raseong Kim, Mark Lundstrom, Notes on Fermi-Dirac Integrals 2nd edition, Network for Computational Nanotechnology Purdue University, June 27, 2008

[2] N.N. Kalitkin, L.V. Kuzmina, Matematicheskoe modelirovanie v nizkotemperaturnoi plazme. Entsiklopediya nizkotemperaturnoi plazmy, 2008

[3] L.V. Kuzmina, Chislennyi raschët termodinamicheskikh funktsii veschestva v statisticheskoi modeli atoma s kvantovo-obmennymi popravkami, Kandidat. dissert., IPM AN SSSR, 1978

[4] N.N. Yanenko, “Asimptoticheskie i priblizhennye formuly dlya davleniya i vnutrennei energii veschestva v obobschennoi modeli atoma Tomasa–Fermi”, [Rabota 1958 goda], Izbrannye trudy, Nauka, M., 1991, 317–352

[5] J. McDougall and E.C. Stoner, “The Computation of Fermi-Dirac Functions”, Phil. Trans. Roy. Soc. London, 237 (1938), 67–104 | DOI

[6] M. Goano, “Algorithm 745: Computation of the Complete and Incomplete Fermi-Dirac Integral”, ACM Trans. Math. Softw., 21 (1995), 221–232 | DOI | Zbl

[7] L.D. Cloutman, “Numerical evaluation of the Fermi-Dirac integrals”, Astrophysical J. Suppl. Series, 71 (1989), 677–699 | DOI

[8] A.J. Macleod, “Algorithm 779: Fermi-Dirac Functions of Order $-1/2$, $1/2$, $3/2$, $5/2$”, ACM Trans. Math. Softw., 24, 1–12 | DOI | Zbl

[9] J.P. Cox and R.T. Giuli, Principles of Stellar Structures, v. 2, Applications to Stars, Gordon and Beach, New York, 1968

[10] (The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers) http://www.gnu.org/s/gsl

[11] W.J. Cody, H.C. Thacher Jr., Rational Chebyshev Approximations for Fermi-Dirac Integrals of Orders $-1/2$, $1/2$ and $3/2$, U.S. Atomic Energy Commission, 1966