The ``error function'' encountered in integrating the Gaussian Distribution.
(1) | |||
(2) | |||
(3) |
(4) |
(5) | |||
(6) |
(7) |
(8) |
(9) |
(10) |
(11) |
(12) |
(13) |
For , erf may be computed from
(14) | |||
(15) | |||
(16) | |||
(17) |
(18) |
(19) |
(20) |
(21) |
A Complex generalization of
is defined as
(22) | |||
(23) | |||
(24) |
See also Dawson's Integral, Erfc, Erfi, Gaussian Integral, Normal Distribution Function, Probability Integral
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Error Function'' and ``Repeated Integrals of the Error Function.''
§7.1-7.2 in Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 297-300, 1972.
Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., p. 16, 1990.
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 568-569, 1985.
Spanier, J. and Oldham, K. B. ``The Error Function
and Its Complement
.''
Ch. 40 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 385-393, 1987.
© 1996-9 Eric W. Weisstein