# [SciPy-user] complex error function in scipy.special

morovia morovia at rediffmail.com
Fri Mar 3 12:40:10 CST 2006

```Thanks for the replies.
wofz(z)is the one I was looking for.

On Fri, 03 Mar 2006 Arnd Baecker wrote :
>On Fri, 3 Mar 2006, morovia wrote:
>
> >
> > Hello,
> >
> > I would like to know whether complex error function which can accept complex argument is implemented in scipy.special.
> >
> > w(z) = i/pi*int(exp(-t**2)/(z-t))dt   limits: -Inf to Inf
> >
> > where z is complex.
>
>What is implemented is this one:
>
>In [1]: import scipy.special
>In [2]: scipy.special.erf?
>Type:           ufunc
>String Form:    <ufunc 'erf'>
>Namespace:      Interactive
>Docstring:
>     y = erf(x) y=erf(z) returns the error function of complex argument
>defined as
>     as 2/sqrt(pi)*integral(exp(-t**2),t=0..z)
>
>which is related to the above w(z), see
>Abramowitz/Stegun, 7.1.3 and 7.1.4.:
>   http://www.math.sfu.ca/~cbm/aands/page_297.htm
>However, I am not sure if using these relations is the best way.
>
>Wait - there is also
>
>In [6]: scipy.special.wofz?
>Type:           ufunc
>String Form:    <ufunc 'wofz'>
>Namespace:      Interactive
>Docstring:
>     y = wofz(x) y=wofz(z) returns the value of the fadeeva function for
>complex argument
>     z: exp(-z**2)*erfc(-i*z)
>
>So this looks like the one you are looking for.
>(as usual: better compare the results for some known values).
>
>Best, Arnd
>
>
>

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