On Tue, 2014-12-23 at 04:12 -0800, Anton Shterenlikht wrote:
> >From: Van Snyder <[log in to unmask]>
> >
> >Even though Don Amos had published ACM TOMS algorithm 644 in 1986, with
> >remarks to improve it in 1990 and 1995, there was sentiment that
> >extending beyond real arguments and integer orders would have resulted
> >in the proposal being rejected as too much work for implementers.
>
> I'm confused. 644 does indeed
> include algorithms for complex arguments [1,2].
> These went into Slatec, and I still use them,
> just checked ZBESJ [3] with complex args yesterday.
Right. I wrote "Even though." The algorithms and code existed.
Intrinsic Bessel functions of complex argument were nonetheless not
added to the Fortran standard, for the reasons mentioned.
> >Algorithm 831, to compute modified Bessel functions (K and I) for pure
> >imaginary order and positive real argument appeared in 2004.
> >
> >Algorithm 877, to compute cylindrical Bessel functions (J, N, H(1) and
> >H(2)) for complex order and positive real argument appeared in 2008.
>
> There might be better algorithms, sure.
>
> >It was considered to be better to have Bessel functions for real
> >argument and non-negative integer order, rather than not to have any.
>
> ok
>
> Anton
>
> [1] http://prod.sandia.gov/techlib/access-control.cgi/1985/851018.pdf
> [2] Algorithm 644: A portable package for Bessel functions of a complex
> argument and nonnegative order, D. E. Amos, ACM Transactions on
> Mathematical Software (TOMS) Volume 12 Issue 3, Sept. 1986, Pages 265-273
> [3] netlib.org/slatec/src/zbesj.f
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