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News for R Package Bessel

Using cospi(nu) instead of cos(pi*nu), for negative nu, both in BesselJ() and BesselY() may increase accuracy.

The exponential rescaling for the asymptotic version of the I() function has been changed (for non-real complex arguments) to be compatible to the scaling for BesselI().

deprecate bI() to use besselIs() instead – enable log = TRUE option and test it.
new besselJs(), i.e., Taylor series for J_n(x); using lssum() for alternating exp/log sum, also works with Rmpfr's mpfr() high precision numbers.
use C routine registration, adding safety and a bit of speed.
improved documentation for Bessel functions Ai,Bi, H, I,J,K,Y.
besselI.nuAsym() and besselK.nuAsym() now allow maximal k.max = 5 (instead of 4).
new besselKasym() (9.7.2 of A.&S. p.378).
All the TOMS 644 routines get an optional argument verbose indicating the verbosity level of output notably from C code. The output itself may change and is not part of the API.

fix BesselI(<cmplx>, nu < 0, expo..=TRUE) bug thanks to Hiroyuki Kawakatsu.
better warning message (r29).
the TOMS 644 routines Bessel[HIYJK] and Airy[AB] now all return NaN with a warning instead of stopping with an error in case of low level error ierr == 4.
BesselK(0,*) is zero now, and BesselH(m, z=0,..) returns Inf/NaN combinations. Both no longer end with an error (from ierr == 1).
BesselK(<negative>, 3) and BesselJ(*) now also return the correct imaginary part instead of just a numeric value.
besselIs(z, nu) now also works for complex z.

BesselY(0, nu) should not give an error message from zbesy(), but either -Inf (real 0) or something like "Inf + NaN i".
Cosmetic, mainly for R CMD check

besselI.nuAsym() and besselK.nuAsym() asymptotic versions for large nu and/or x