Erfc
The ``complementary error function''
 |  |  | (1) |
 |  | (2) | |
|  | (3) |
where
is the incomplete Gamma Function. It has the values | |  | (4) |
 | |  | (5) |
 | (6) |
 | |  | (7) |
 | |  | (8) |
A generalization is obtained from the differential equation
 | (9) |
 | (10) |
is the erfc integral. For integral 
, | |  | (11) |
|  | (12) |
The definition can be extended to
and 0 using | |  | (13) |
 | |  | (14) |
See also Erf, Erfi
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Repeated Integrals of the Error Function.'' §7.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 299-300, 1972.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function.'' §6.2 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 209-214, 1992.
Spanier, J. and Oldham, K. B. ``The Error Function 
and Its Complement 
'' and ``The 
and 
and Related Functions.'' Chs. 40 and 41 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 385-393 and 395-403, 1987.
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