Re: Integration of the oscillating function

Hi Andrey,

currently in ROOT there is no method for an oscillatory function. There is one in GSL, see

   http://www.gnu.org/software/gsl/manual/html_node/QAWO-adaptive- integration-for-oscillatory-functions.html

but is not yet implemented in the Integrator class of MathMore. If needed, I could add it for the next ROOT release.

However if you want just to integrate the Bessel function, analytical formula exist in terms of other functions, for example for J0(z) see

http://functions.wolfram.com/BesselAiryStruveFunctions/BesselJ/ 21/01/01/0003/

also a J0(z) can be approximate for large z values as:

  cyl_bessel_j(0,z) ~ sqrt(2.0/( PI*x) ) * cos(x- PI/4 )

Cheers

  Lorenzo

On Dec 12, 2006, at 5:23 PM, andreyk1_at_post.tau.ac.il wrote:

>
> Dear Rooters!
>
> I have to perform a calculation of the integral of oscillating
> function, namely
> J0(z) (Bessel J0). How should I integrate it (in this case the
> integration is
> over "z" variable) in order to obtain a proper result?
>
> For example, in Matematica there is a method of integration which
> is called
> "Oscillatory method" which allows to integrate such oscillating
> functions.
>
> *I use TF1 class with "IntegralMultiple" function
> --
> Sincerely,
>
> Andrey K.
>
> *************************************************************
> * Andrey Kormilitsin * *
> * * *
> * Department of * *
> * Particle Physics * *
> * School of Physics * Tel: ++ 972- 3 - 640 7954 (o) *
> * Tel Aviv University * *
> * Ramat Aviv,Tel Aviv * E-mail: andreyk1_at_post.tau.ac.il *
> * 69978, ISRAEL * *
> * * *
> *************************************************************
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Received on Wed Dec 13 2006 - 10:24:25 MET