#15024: Add Hankel functions and make spherical Bessel and Hankel functions
symbolic
-------------------------------------+-------------------------------------
       Reporter:  eviatarbach        |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.3
      Component:  symbolics          |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Eviatar Bach,      |    Reviewers:  Paul Masson
  Ralf Stephan                       |
Report Upstream:  N/A                |  Work issues:
         Branch:  u/rws/15024        |       Commit:
                                     |  28606307034dd394ec39a74508e05442cb4b4fc9
   Dependencies:  #18257             |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by paulmasson):

 * commit:  ab6006d7d04c8add865c48b1ecd0132a330bebd0 =>
     28606307034dd394ec39a74508e05442cb4b4fc9


Comment:

 Doctests pass and documentation builds. Numerics look good. A few problems
 resulting from the merge conflict resolution:

 1) A line has been modified in `hypergeometric.py`. This modification
 appears to be inaccurate and has the wrong variable anyway. Please remove
 the condition `x>0` on `hypergeometric_U`.

 2) The definition of the spherical Bessel function of the second kind has
 been left behind in `special.py` after the definition of spherical
 harmonics. This one needs to be deleted since it's already in `bessel.py`.

 3) The evaluation of spherical harmonics has changed. I'm assuming this is
 because `meval` is gone, but please confirm. This change has no apparent
 problems.

 4) There are doctests added to the complete elliptic integral which are
 outside this ticket. Since they pass I'm fine leaving them here, but let
 me know that they are included just to avoid an extra ticket.

 ----
 New commits:
 
||[https://git.sagemath.org/sage.git/commit?id=28606307034dd394ec39a74508e05442cb4b4fc9
 2860630]||{{{Merge branch 'develop' into tmp02}}}||

--
Ticket URL: <https://trac.sagemath.org/ticket/15024#comment:56>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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