R devel - Feb 2009 - besselI inaccurate for negative integer order (PR#13556)

Full_Name: Jerry W. Lewis
Version: 2.8.1
OS: Windows XP Professional
Submission from: (NULL) (198.180.131.16)


It should be the case that
  besselI(x,-nu) == besselI(x,nu) == besselI(x,abs(nu))
for integer nu, yet R currently can return ridiculous values when nu is a
negative integer.

For instance, besselI(9.6,-44) returns -234626490 instead of the correct value
of 5.9041042646307223e-25, while besselI(9.6,44) gives essentially machine
accuracy.

This is more than an idle mathematical curiosity, since one consequence is that
dskellam in the VGAM package can return values <0 or >1.

>>>>> "JL" == Jerry Lewis <Jerry.Lewis at
biogenidec.com>
>>>>>     on Thu, 26 Feb 2009 16:15:11 +0100 (CET) writes:
    JL> Full_Name: Jerry W. Lewis
    JL> Version: 2.8.1
    JL> OS: Windows XP Professional
    JL> Submission from: (NULL) (198.180.131.16)


    JL> It should be the case that
    JL> besselI(x,-nu) == besselI(x,nu) == besselI(x,abs(nu))
    JL> for integer nu, yet R currently can return ridiculous values when nu
is a
    JL> negative integer.

    JL> For instance, besselI(9.6,-44) returns -234626490 instead of the
correct value
    JL> of 5.9041042646307223e-25, while besselI(9.6,44) gives essentially
machine
    JL> accuracy.

Yes.  I have committed a bug-fix to both R-patched and R-devel.

Thank you for the report!
Martin Maechler, ETH Zurich


    JL> This is more than an idle mathematical curiosity, since
    JL> one consequence is that dskellam in the VGAM package can
    JL> return values <0 or >1.