As a general goal we could try to have bigfloat evaluation
of every function. This can be done by mapping to a bigfloat
evaluation of 2F3 hypergeometric functions, which I suspect
is how Mathematica does it. The programs may not achieve
adequate relative error at critical points (e.g. zeros of
Bessel functions).
RJF
Raymond Toy wrote:
>>>>>>"Barton" == Barton Willis <willisb@unk.edu> writes:
>>>>>>
>>>>>>
>
> Barton> (2) It seems that bessel_j and friends do not evaluate to a float for
> Barton> either big float or double-float complex arguments. Does slatec handle
> Barton> evaluation of the bessel functions off the real-axis? If it does, that
> Barton> would be a nice extension.
>
>They definitely don't handle bigfloats. I've been thinking about how
>to do it, but haven't done anything yet, because I'd want them to
>evaluate them to bigfloat accuracy. Smashing the bigfloats to
>double-floats is doable, but seem a bit of a hack for a symbolic
>package like maxima. :-) I think the only way to compute them is to
>use series evaluation and asymptotic expressions. A lot of work, and
>I don't know anyone who's asked for bigfloat bessel functions.
>
>Some of the changes I have will compute the Bessel functions for
>complex args, but not complex orders. Slatec doesn't seem to have any
>routines for complex orders, and I haven't really found any either.
>
>Ray
>