[SciPy-Dev] PR adding vectorized spherical Bessel functions

[Ted Pudlik]

Hello,

I started a pull request <https://github.com/scipy/scipy/pull/5623>
providing vectorized implementations of four spherical Bessel functions
(jn, yn, in, kn) and their derivatives.  This is my first large pull
requests, so I would be grateful for any comments!

Highlights:

   1. Speedup of about an order of magnitude relative to `np.vectorize`
   (generally more, except for jn for real argument).
   2. Recursion largely replaced with the relationship to cylindrical
   Bessel functions <http://dlmf.nist.gov/10.47.ii>, which resolves
   accuracy issues for large argument (see gh-1641
   <https://github.com/scipy/scipy/issues/1641>, gh-2165
   <https://github.com/scipy/scipy/issues/2165> for jn at large real
   argument, but similar problems existed for yn and kn at large complex
   argument).
   3. More careful treatment of 0, infinity, and overflow.  (E.g.,
   sph_kn(125, 0.1) = inf, not 0; yn(5, 0) = -inf, not -10**300.)

Best wishes,
Ted
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