Dear Brian, Actually, it should also be correct for functions which are non-zero at the center. I don't know about the discrete algorithm used in dht, but for instance doing the same calculations using Mathematica and implementing a numerical integration works. This is not an option though, because it is too slow.
Something else I thought of is that, maybe the steps in space are too big. I'll send some code. Regards, Benno Ps. about the code. It calculates the 0^th order Hankel transform and commented out is a part that multiplies the function in Hankel space by k^2, such that when you transform back you get the second derivative. On 23 Dec 2010, at 15:04, Brian Gough wrote: > At Wed, 22 Dec 2010 15:23:34 +0100, Benno Rem wrote: >> I noticed that, as soon as I try to do a Hankel Transform (nu = 0) >> on a gaussian of the form exp( - pi * r^2 ), transform it back and >> multiply by the factor Jzero0(0,N)^2, that I don't get the exactly >> same function back. Actually, the function that is returned is >> scaled by a factor 1.00391 with respect to the original function. >> >> For just one transform it can be considered as just a numerical >> error, but as soon as I try to do some more complicated stuff I get >> strong abbreviations from the real result. >> >> I'm not sure if this is a bug, or just a misunderstanding of the >> concept, but it would help me a lot if someone could give me an >> idea. > > Hello, > > I think the transform is only exact for functions that are zero at the > boundaries. If this does not explain the discrepancy could you send > an example program and output which demonstrates the problem. Thanks. > > -- > Brian Gough > Benno REM [email protected] ------------------------------------------ Département de Physique de l'Ecole Normale Supérieure Laboratoire Kastler Brossel 24 rue Lhomond 75005 Paris Phone office: +33 1 44 32 33 03 Phone lab: +33 1 44 32 33 08 Fax office: +33 1 44 32 34 34 _______________________________________________ Bug-gsl mailing list [email protected] http://lists.gnu.org/mailman/listinfo/bug-gsl
