Dieter Kaiser wrote:
> Now we calculate the Bessel functions for negative argument and order and we
> have to look more carefully to the different special cases for zero argument. As
> a reference I used the specialized values from functions.wolfram.com. I added
> the special case for a complex order too. Is this useful? Is it correct to
>
I think it is very useful.
> return the value '$infinity in the case of a complex infinity? Or should we
> generate a domain-error?
>
Not sure. It seems the numeric code generates a domain-error when doing
numerical evaluation. Like cot(0.0) and such. cot(0) can return
infinity or und, but it doesn't right now. We might want to discuss
this further in the context of all of the special functions.
> Further sligtly improvements can be done for the other Bessel functions too. I'm
> working on this task.
>
> A next step will be the implementation of Bessel functions with complex order
> and the improvement of the scaled Bessel functions.
>
>
Do you have a reference on computing Bessel functions of complex order.
A couple of books I have just use the power series or asymptotic series
to evaluate. But the accuracy is not so good then.
The scaled Bessel functions aren't that important. I haven't heard of
anyone using them; they were implemented long ago with names you would
never guess. (I think gn(x) was the scaled_bessel_i(n,x).)
Ray