>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.
>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
