On Thu, Apr 08, 2021 at 07:17:42PM +0200, Kurt Pagani wrote: > Maybe you are already aware of > > COMPUTATION OF BESSEL AND AIRY FUNCTIONS AND OF RELATED GAUSSIAN QUADRATURE > FORMULAE by WALTER GAUTSCHI > https://www.cs.purdue.edu/homes/wxg/selected_works/section_02/169.pdf
Thanks for reference. > The code is in Fortran though. > https://www.cs.purdue.edu/archives/2001/wxg/codes/ > > IMO it would be easier, however, if we took it from GSL: > https://www.gnu.org/software/gsl/doc/html/specfunc.html > Bill wrote an interface: > https://github.com/billpage/gsla/blob/master/gsl.lisp Both ilutrate what I wrote: Gautschi has 0<p<1 and real x. GSL has real arguments. As I wrote, there are good looking implementations for real p (and complex x). A have a toy multiple precision implementation, it is fast enough if arguments are resonably small. OTOH our Bessel J and H01 also seem to havve resonable accuracy when arguments are small. The problem is large arguments. Also, it would be silly to use multiple precision implementation to get double accuracy, but do not provide real multiple precision implementation. But with multiple precision results problem of large arguments gets worse... Just to be clear: in case of Airy we can try to hide bug, that is provide low accuracy version. That would be easy, but the accuracy problem would come back later. The point is to sort out the mess so that it works. And ATM it seem that nobody else did this in really satisfactory way, so appearently we should be first to do this. -- Waldek Hebisch -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/20210408180649.GA27175%40math.uni.wroc.pl.
