>> Do you think some of the functions should be rather implemented in mpmath?
>
> which functions do you mean exactly? The jn_zeros? I don't mind. But
> mpmath is sometimes very slow, e.g. I want to be able to use scipy
> optionally. It can be in mpmath, I have no problems with that. But
> then you would need the jn() function too in there, but that one uses
> sympy a lot, so I don't think it's that easy.

Bessel function zeros, along with a couple of other inverse functions,
will benefit greatly from the more generic high-level interface
being added to mpmath.

Basically, the first 16 digits can be computed entirely using machine
precision arithmetic, and then in the high precision case, mpmath can
use the machine precision estimate as the initial argument to
findroot.

Fredrik

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