This is the mail archive of the
gsl-discuss@sources.redhat.com
mailing list for the GSL project.
Re: some problem with QAWF integration
- From: Vladimir Savichev <vlad at ariel dot phys dot wesleyan dot edu>
- To: xieq at yahoo dot com
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Thu, 11 Apr 2002 17:38:55 -0400
- Subject: Re: some problem with QAWF integration
I think a simpliest thing to do is to rescale
w*x => x. If you choose to break into to peaces
then do it for the first part
\int_{0} ^{pi/w} f(x)*sin(w*x)/x dx => \int_{0} ^{pi} f(x/w)*sin(x)/x dx
If w gets really big you can get an answer in almost analytical form
I = I_0*f(0) + I_1*f'(0)/w + I_2*f"(0)/2w^2+... ,
where I_i are
I_0 = \int_{0} ^{pi} sin(x)/x dx, I_1 = \int_{0} ^{pi} sin(x) dx, I_2 = \int_{0} ^{pi} x*sin(x) dx
You can scale \int_{pi/w} ^{inf} peace as well or integrate it as it is. It relies on
f(x) profile .
Hope it helps,
Vlad