Re: [Help-gsl] Integration involving Bessel Function

[Gideon Simpson]

I'll take this opportunity to follow up on something.  Rokhlin developed a fast 
hankel transform using a mixture of the fft and fast multipole, see 

http://www.cs.yale.edu/publications/techreports/tr1045.pdf

This would be a very useful tool to have, but no one seems to have distributed 
code for it.  I've been looking for a collaborator/student who'd be interested 
in developing it.  It would make a nice addition to the GSL.

-gideon

On Jun 6, 2010, at 11:35 PM, Gideon Simpson wrote:

> What you're trying to do is perform a Hankel transform of order 0 at wave 
> number 1.  See http://en.wikipedia.org/wiki/Hankel_transform.  I think you're 
> best bet, off the shelf, is to use the DHT, the discrete hankel transform, 
> which is part of the GSL library.  If your function F(x) decays sufficiently 
> rapidly, the DHT should be satisfactory.
> 
> -gideon
> 
> On Jun 2, 2010, at 6:33 AM, address@hidden wrote:
> 
>> Dear Sir,
>> 
>> I am a beginer with gsl and I am trying to do an integration of the form:
>> 
>> \int_0^\infty [ x J0(x) F(x) ].
>> 
>> J0(x) being oscillatory makes the integrtal +ve and -ve within its
>> consecutive zero's. Form of F(x) is such that the overall integrand is a
>> decaying function of x.
>> 
>> How to handle this type of integration using gsl.
>> 
>> I tried using "gsl_integration_qag", but its not giving the correct results.
>> 
>> with best regards,
>> Prithwish
>> 
>> _______________________________________________
>> Help-gsl mailing list
>> address@hidden
>> http://lists.gnu.org/mailman/listinfo/help-gsl
> 
> 
> _______________________________________________
> Help-gsl mailing list
> address@hidden
> http://lists.gnu.org/mailman/listinfo/help-gsl