Dieter Kaiser wrote:
> I have implemented the improvemtents suggested for bessel_j for the other Bessel
> functions too.
>
I'll integrate these changes soon. Thanks for working on this!
> 1.
> Complete handling of the different cases of zero argument.
> The return values includes the constants INF, MINF and INFINITY. Is that useful
> for Maxima?
>
> With this changes you get e.g.
>
> limit(bessel_y(2,x),x,0) ---> INFINITY
> limit(bessel_k(0,x),x,0) ---> INF
>
>
As limits, these are good. Not quite sure about the first though. I
think Maxima usually assumes real limits, so maybe und or ind would be
better.
What does maxima say without the limit? That is bessel_k(0,0) -> ?
And bessel_y(2,0)?
> There is one open question for me. For negative arg we use the analytic
> continuation formulars. The exception is bessel_i. For this case we use for
> negative arg the definition and calculate the values with the help of the
> bessel_j function. So the algorithm is more simple in this case, but it may be
> better to implement the continuation formula too.
>
I suspect the formula used was whatever seemed easiest to implement or
understand. Or maybe even whatever formula came first in A&S.
If there's a case where the continuation formula is more accurate or
something, then we should change it. If not, then there's no pressing
reason.
Ray