From: Rene Brun <Rene.Brun_at_cern.ch>

Date: Wed, 13 Dec 2006 11:11:12 +0100

//see doc of TF1::Integral and TF1::Absvalue TF1::AbsValue(kTRUE);

f1->DrawIntegral();

}

Date: Wed, 13 Dec 2006 11:11:12 +0100

Andrei,

The besselJ0 (and others) functions are available in TMath. You can
compute these functions,

their integral, and draw them. See an example below

Rene Brun

void J0() {

//example showing a BesselJ0(x) function and its integral

TF1 *f1 = new TF1("f1","TMath::BesselJ0(x)",-1,6); TCanvas *c1 = new TCanvas("c1","c1",800,1000);

c1->Divide(1,2); c1->cd(1); f1->Draw(); c1->cd(2);

//see doc of TF1::Integral and TF1::Absvalue TF1::AbsValue(kTRUE);

f1->DrawIntegral();

}

Lorenzo Moneta wrote:

*> 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 * **

*>> * * **

*>> **************************************************************

*>>*

*>>*

*>> ----------------------------------------------------------------*

*>> This message was sent using IMP, the Internet Messaging Program.*

*>>*

*>>*

Received on Wed Dec 13 2006 - 11:11:23 MET

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