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Issue No.04 - July/August (2010 vol.12)
pp: 84-88
ABSTRACT
<p>A new exact representation of the error function of real arguments justifies an accurate and simple analytical approximation.</p>
INDEX TERMS
analytics, error function
CITATION
Mohankumar Nandagopal, Soubhadra Sen, Ajay Rawat, "A Note on the Error Function", Computing in Science & Engineering, vol.12, no. 4, pp. 84-88, July/August 2010, doi:10.1109/MCSE.2010.79
REFERENCES
1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, 1965.
2. W. Cody, "Rational Chebyshev Approximations for the Error Function," Mathematics of Computation, vol. 23, no. 107, 1969, pp. 631–638.
3. W. Gautschi, "Efficient Computation of the Complex Error Function," SIAM J. Numerical Analysis, vol. 7, 1970, pp. 187–198.
4. M. Mori, "A Method for Evaluation of the Error Function of Real and Complex Variable with High Relative Accuracy," Publications of Research Inst. Mathematical Science (RIMS), Kyoto Univ., vol. 19, 1983, pp. 1081–1094.
5. P. Van Halen, "Accurate Analytical Approximations for Error Function and its Integral," Electronics Letters, vol. 25, no. 9, 1989, pp. 561–563.
6. J.D. Williams, "An Approximation to the Probability Integral," Annals Mathematical Statistics, vol. 17, no. 3, 1946, pp. 363–365.
7. R. Menzel, "Approximate Closed Form Solution to the Error Function," American J. Physics, vol. 43, no. 10, 1975, pp. 366–367.
8. S. Kalkaja, "Approximation for Error Function of Real Argument," 2005; www.student.oulu.fi/~saulikalerrorf.pdf.
9. D.V. Widder, Advanced Calculus, Prentice-Hall, 1961.
10. D.S. Mitronovic, Analytic Inequalities, Springer-Verlag, 1970.
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