[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
More information about the SciPy-user
mailing list