Implement complex-order Bessel functions

[ariel]

I have noticed that the Bessel function yv does not accept complex arguments, is there a bug or is it meant to be like that? If so, is there a patch or package to compute Bessel functions of second kind with complex arguments?

Thanks in advance

Ariel

[pv]

Bessel functions of complex argument work,

>>> import scipy, scipy.special as sc
>>> scipy.__version__
'0.7.1'
>>> sc.yv(3, 1+2j)
(0.29015329423954583-0.21211877047925784j)

There's no implementation of complex-order Bessel functions at the moment, however,

>>> sc.yv(3j, 1+2j)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: function not supported for these types, and can't coerce safely to supported types

[pv]

The most direct way to complex-order Bessels is probably via adding complex-a or a,b support in hyp0f1 or hyp1f1. Also these currently accept only real a,b (although they do accept complex z).