Unified treatment for accurate and fast evaluation of the Fermi－Dirac functions

doi:10.1088/1674-1056/19/5/050501

摘要/Abstract

摘要： A new analytical approach to the computation of the Fermi-Dirac (FD) functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.

Abstract: A new analytical approach to the computation of the Fermi-Dirac (FD) functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.

Key words: statistical, semiconductors, plasma physics, nuclear physics

中图分类号: (Fermion systems and electron gas)

05.30.Fk

02.30.Lt (Sequences, series, and summability) 02.30.Mv (Approximations and expansions) 02.30.Sa (Functional analysis)

I.I.Guseinov, B.A.Mamedov. Unified treatment for accurate and fast evaluation of the Fermi－Dirac functions[J]. 中国物理B, 2010, 19(5): 50501-050501.

I. I. Guseinov and B. A. Mamedov. Unified treatment for accurate and fast evaluation of the Fermi－Dirac functions[J]. Chin. Phys. B, 2010, 19(5): 50501-050501.

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