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Re: [Help-gsl] Integration involving Bessel Function
From: |
Gideon Simpson |
Subject: |
Re: [Help-gsl] Integration involving Bessel Function |
Date: |
Mon, 7 Jun 2010 10:23:50 -0400 |
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
>>
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>
>
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