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Re: [Help-gsl] Integration involving Bessel Function

From: ptribedy
Subject: Re: [Help-gsl] Integration involving Bessel Function
Date: Fri, 4 Jun 2010 14:43:53 -0400
User-agent: SquirrelMail/1.4.19

Dear Sir,
thank you for the suggestion.

Yes, I tried "gsl_integration_qagiu" , it also couldn't handle the
oscillation and finally giving a very large +ve or -ve value.

I am doing multiple integrations(using say gsl_integration_qag) between
the zero's of J0(x) and summing up the series using some force convergence
method. Its is very slow method.

My integral is :

I(k)= \int_0^\infty [dx x J0(kx) F(x) ].

comes from

I(k)= 1/(2pi)*\int_0^\infty [ d^2x exp(i k.x) F(x)]

which is has a form very similar to a Fourier-Transform integration.

is there any other efficient method to handle such integral?

> At Wed, 2 Jun 2010 06:33:16 -0400,
> address@hidden wrote:
>> 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.
> Did you try gsl_integration_qagiu (infinite upper limit)?

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