SciPy

scipy.special.erf

scipy.special.erf(z) = <ufunc 'erf'>

Returns the error function of complex argument.

It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).

Parameters :

x : ndarray

Input array.

Returns :

res : ndarray

The values of the error function at the given points x.

See also

erfc, erfinv, erfcinv

Notes

The cumulative of the unit normal distribution is given by Phi(z) = 1/2[1 + erf(z/sqrt(2))].

References

[R200]http://en.wikipedia.org/wiki/Error_function
[R201]Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972. http://www.math.sfu.ca/~cbm/aands/page_297.htm
[R202]Steven G. Johnson, Faddeeva W function implementation. http://ab-initio.mit.edu/Faddeeva