#11143: define symbolic functions for exponential integrals
-------------------------------------------------------------+--------------
       Reporter:  kcrisman                                   |         Owner:  
benjaminfjones                    
           Type:  defect                                     |        Status:  
needs_review                      
       Priority:  major                                      |     Milestone:  
sage-5.1                          
      Component:  symbolics                                  |    Resolution:   
                                 
       Keywords:  ei Ei special function maxima sd32 sd40.5  |   Work issues:   
                                 
Report Upstream:  N/A                                        |     Reviewers:  
Burcin Erocal, Karl-Dieter Crisman
        Authors:  Benjamin Jones                             |     Merged in:   
                                 
   Dependencies:                                             |      Stopgaps:   
                                 
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Comment (by dsm):

 Thanks, kcrisman.  Since after real-world discussions it appears that the
 integration difficulty is another Maxima quirk, I don't think we should
 hold up approving this, especially because it can be worked around.  I do
 think it's worth warning the user, and the example will serve as a
 reminder to us that it can be removed when we update to a version of
 Maxima which finally fixes it, 'cause the doctest will fail.

 So I propose adding the following to EXAMPLES for sinh_integral:

 {{{

     Note that due to some problems with the way Maxima handles these
     expressions, definite integrals can sometimes give unexpected
     results (typically when using inexact endpoints) due to
     inconsistent branching::

         sage: integrate(sinh_integral(x), x, 0, 1/2)
         -cosh(1/2) + 1/2*sinh_integral(1/2) + 1
         sage: integrate(sinh_integral(x), x, 0, 1/2).n() # right
         0.125872409703453
         sage: integrate(sinh_integral(x), x, 0, 0.5).n() # wrong!
         0.125872409703453 + 1.57079632679490*I

 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11143#comment:53>
Sage <http://www.sagemath.org>
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