# scipy.special.erf#

scipy.special.erf(z, out=None) = <ufunc 'erf'>#

Returns the error function of complex argument.

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

Parameters:
xndarray

Input array.

outndarray, optional

Optional output array for the function values

Returns:
resscalar or ndarray

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

Notes

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

References

[2]

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

[3]

Steven G. Johnson, Faddeeva W function implementation. http://ab-initio.mit.edu/Faddeeva

Examples

```>>> import numpy as np
>>> from scipy import special
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-3, 3)
>>> plt.plot(x, special.erf(x))
>>> plt.xlabel('\$x\$')
>>> plt.ylabel('\$erf(x)\$')
>>> plt.show()
```