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Variable Precision Algorithm for the Numerical Computation of the Fermi–Dirac Function ℱj(x) of Order j=−3/2

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Abstract

The purpose of this technical note is to present a piecewise Chebyshev expansion for the numerical computation of the Fermi–Dirac function ℱ−3/2(x), −∞<x<∞. The variable precision algorithm we given automatically adjusts the degrees of the Chebyshev expansions so that ℱ−3/2(x) can be efficiently computed to d significant decimal digits of accuracy, for a user specified value of d in the range 1≤d≤15.

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REFERENCES

  • Arkinson, K. E. (1989). An Introduction to Numerical Analysis, Wiley, New York.

    Google Scholar 

  • Clenshaw, C. W. (1962). Mathematical Tables, Volume 5, Chebyshev Series for Mathematical Functions. National Physical Laboratory, Her Majesty's Stationary Office, London.

    Google Scholar 

  • Dingle, R. B. (1957). The Fermi-Dirac Integrals. Appl. Sci. Res. B 6, 225–239.

    Google Scholar 

  • Fike, C. T. (1968). Computer Evaluation of Mathematical Functions, Prentice-Hall, Englewood Cliffs.

    Google Scholar 

  • Goano, M. (1995). Algorithm 745: Computation of the Complete and Incomplete Fermi-Dirac Integral. ACM Trans. Math. Software 21, 221–232.

    Google Scholar 

  • Lether Lether, F. G. et al. (1987). An algorithm for the numerical evaluation of the reversible Randles-Sevcik function. Comput. Chem. 11, 179–183.

    Google Scholar 

  • MacLeod, A. (1993). A note on the Randles-Sevcik function in electrochemistry. Appl. Math.Comp. 57, 305–310.

    Google Scholar 

  • MacLeod, A. (1998). Algorithm 779: Fermi-Dirac functions of order &-1/2, 1/2, 3/2, 5/2. ACM TOMS 24, 1–12.

    Google Scholar 

  • McDougall, J. C. et al. (1938). The computation of Fermi-Dirac functions. Phil. Trans. Roy. Soc. London 237, 67–104.

    Google Scholar 

  • Natarajan, A. et al. (1997). An algorithm for the numerical evaluation of the Randles-Sevcik function. Computers Chem. 21, 315–318.

    Google Scholar 

  • Scraton, R. E. (1970). A method for improving the convergence of Chebyshev series. Computer Journal 13, 202–203.

    Google Scholar 

  • Trellakis, A. et al. (1997a). Iteration scheme for the solution of the two-dimensional Schrödinger-Poisson equations in quantum structures. J. Appl. Phys. 81, 7880–7884.

    Google Scholar 

  • Trellakis, A. et al. (1997b). Rational Chebyshev approximation for the Fermi-Dirac integral ℱ-3/2. Solid-State Electronics 41, 771-773.

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, Boyd Graduate Research Center, University of Georgia, Athens, Georgia, 30602-7403

    F. G. Lether

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  1. F. G. Lether
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Lether, F.G. Variable Precision Algorithm for the Numerical Computation of the Fermi–Dirac Function ℱj(x) of Order j=−3/2. Journal of Scientific Computing 16, 69–79 (2001). https://doi.org/10.1023/A:1011150530703

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