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

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 function...

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Bibliographic Details
Published in:Chinese physics B 2010-05, Vol.19 (5), p.72-77
Main Authors: Guseinov, I. I, Mamedov, B. A
Format: Article
Language:English
Subjects:
Algorithms
Binomial coefficients
Binomials
Computer simulation
Gamma function
Mathematical analysis
Mathematical models
Simplification
二项式定理
二项式系数
函数表达
狄拉克函数
统一处理
计算结果
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Summary: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 the 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.
ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/19/5/050501