Re: [Help-gsl] Oscillating integral: Product of Bessel functions

[Analabha Roy]

Yeah, I think it's just the Fourier Cosine Transform of In * Kn. I think u
might be better off using a  DFT package here since oscillatory weight
functions generally produce nasty numerical errors and DFT packages handle
those better.




On 3/15/06, Mehmet Suzen <address@hidden> wrote:
>
> I am not sure!
>
> On 3/14/06, Analabha Roy <address@hidden> wrote:
> > Hey isn't that just a fourier cosine ransform of the Bessel Function?
> >
> >  You might want to try using the fftw libs and check that with your QAGS
>
> > result .
> >
> >
> > On 3/9/06, Mehmet Suzen <address@hidden> wrote:
> > > Hi,
> > > Actuall main function looks like
> > >
> > > f = int_{0}^{infty} x * cos(-x*Z) * gsl_sf_bessel_In(m,x*R) *
> > > gsl_sf_bessel_Kn(m+1,x*R)
> > > Z and R parameters. For this also I got problems with QAWO and QAWF
> but
> > > if I use QAGS I can get a result but it is oscillating with increasing
> m.
> > > Any suggestion ?
> > >
> > > Thanks,
> > > Mehmet
> > > On 3/9/06, Inigo Aldazabal Mensa <address@hidden> wrote:
> > > > Hi,
> > > >
> > > > As x->\infty your integrand diverges oscillating something like
> > exponentially,
> > > > as gsl_sf_bessel_In does, and nothing kills this behaviour. Are you
> sure
> > this
> > > > integral should converge?
> > > >
> > > > Regards,
> > > >
> > > > Iñigo
> > > >
> > > > El Jueves, 9 de Marzo de 2006 09:54, Mehmet Suzen escribió:
> > > > > Hello All,
> > > > > I have tried to use QAWO or QAWF for integrating function which is
> > > > > a product of modified bessel functions. Integral looks like
> > > > >  f = int_{0}^{infty} x * cos(-x*Z) * gsl_sf_bessel_In(m,x*R)  dx
> > > > > X and R are parameters.
> > > > > but I am getting  error message ;
> > > > > gsl: qawo.c:436: ERROR: cannot reach tolerance because of roundoff
> > error
> > > > > I have tried different epsabs or TOL, it doesn't help. How do I
> choose
> > > > > right tolerance and bin sizes? And I have seen on the net that
> product
> > of
> > > > > bessel functions are problematic in integration. Any comment would
> be
> > > > > helpful. Cheers,
> > > > > --Mehmet
> > > > >
> > > > >
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> > > --
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> > > --Mehmet Suzen
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