This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Note on the Error Function
July/August 2010 (vol. 12 no. 4)
pp. 84-88

A new exact representation of the error function of real arguments justifies an accurate and simple analytical approximation.

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.

Index Terms:
analytics, error function
Citation:
Mohankumar Nandagopal, Soubhadra Sen, Ajay Rawat, "A Note on the Error Function," Computing in Science and Engineering, vol. 12, no. 4, pp. 84-88, July-Aug. 2010, doi:10.1109/MCSE.2010.79
Usage of this product signifies your acceptance of the Terms of Use.