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

Arnd Baecker arnd.baecker at web.de
Fri Mar 3 12:06:03 CST 2006


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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