[SciPy-User] Bessel function of complex order

[Pauli Virtanen]

Andreas Pritschet <webmaster <at> hasenkopf2000.net> writes:
> I have noticed in the docs and some "bug reports" that Bessel functions
> in SciPy support only real order. But for my work I require a modified
> Bessel function of second kind of complex(!) order for complex values.
> 
> Is in SciPy a chance of calculating something like
> scipy.special.kv(1j*k,1j), whereby k is an array?

You can use `besselk` from the mpmath library. It's arbitrary-precision
code, and will probably be slower roughly by a factor of 1000 than
equivalent compiled  floating point code. That may be fast enough.

Adding complex-order functions present in Scipy requires either 
(i) someone to dig up a license-compatible special function library
that has them, or (ii) someone with sufficient knowledge to write
such a part of such a library. This is somewhat onerous and fiddly
work, and I'm not going promise when (and if) I would work on it.

BTW, if you know good special function libraries with BSD compatible
licenses, please reply!

Scipy is missing a complex domain implementation of some of
the hypergeometric  functions, which would be required for
expressing the complex-order bessels. The implementation for
hypergeometric functions in mpmath IIRC relies on dynamic
adjustment of precision on the fly, and such code cannot
be simply ported for floating point.

-- 
Pauli Virtanen