[Rd] Re Bessel functions of complex argument

[Martin Maechler]

{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.

We have seen several occasions where people had a clear usage
need for them.

{{I have a vague déjà-vue feeling on this whole topic ....}}

Martin Maechler, ETH Zurich