Oh, I must have had some other Fortran code in mind (Gautschi has only $p\in (0,1)$, indeed).
https://jblevins.org/mirror/amiller/ I guess it was the one below, but there are some others (CTRL-F Bessel ...) https://jblevins.org/mirror/amiller/cbsslj.f90 cbsslj.f90 Complex Bessel function J_{\nu}(z) where both the argument, z, and the order, \nu, are complex. Anyway, it makes hardly sense to convert F90 to fricas, but it may be helpful for comparing purposes. On 08.04.2021 20:06, Waldek Hebisch wrote: > 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. > -- 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/425b014f-d3b4-b62f-b694-2c57be034a6e%40gmail.com.
