# 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
xndarray

Input array.

Returns
resndarray

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

1

https://en.wikipedia.org/wiki/Error_function

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

>>> 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()


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