Re Bessel functions of complex argument
On Mon, 10 Mar 2008, Martin Maechler wrote:
{Diverted from an R-help thread}
"Robin" == Robin Hankin <r.hankin at noc.soton.ac.uk>
on Mon, 10 Mar 2008 08:49:06 +0000 writes:
Robin> Hello Baptiste Bessel functions with complex Robin> arguments are not supported in R. Robin> Neither matlab nor the Gnu Scientific Library support Robin> them either. Robin> . . . but . . . Robin> the pari/gp system (released on the GPL) does: Robin> ? besselj(1+I,3) Robin> %3 = 0.6919067491368555819808728680 + 0.4484268613977010268818252591*I Robin> ? Robin> You can access some pari/gp functionality from within R Robin> by using the elliptic package, although unfortunately Robin> its wrapper function, P.pari(), is not quite flexible enough Robin> to deal with besselj(). Robin> I'd be happy to discuss this offline; P.pari() will need only Robin> minor changes to accommodate besselj(). Hi Robin, have you looked at *how* pari/gp does this? If they have a C routine, it might be worth considering to add ``the'' complex Bessel functionality to R.
To an R package, surely? They hardly seem important enough for base R. There are C implementations in several places, e.g. ACM algorithm 644 (also netlib.org/amos).
We have seen several occasions where people had a clear usage
need for them.
{{I have a vague d?j?-vue feeling on this whole topic ....}}
Martin Maechler, ETH Zurich
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595