#4102: make bessel_J symbolic
----------------------------------+-----------------------------------------
       Reporter:  jwmerrill       |         Owner:  burcin  
           Type:  enhancement     |        Status:  new     
       Priority:  major           |     Milestone:  sage-5.6
      Component:  calculus        |    Resolution:          
       Keywords:                  |   Work issues:          
Report Upstream:  N/A             |     Reviewers:          
        Authors:  Benjamin Jones  |     Merged in:          
   Dependencies:                  |      Stopgaps:          
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Comment (by benjaminfjones):

 Replying to [comment:17 kcrisman]:
 > > >  * Maybe Python 3 string formatting?  Though I am not sure how to
 mix that with LaTeX braces.
 > >
 > > ???
 >
 > Such as [http://docs.python.org/3.1/library/stdtypes.html#str.format
 this] and [http://docs.python.org/3.1/library/string.html#formatstrings
 this].  Just for forward-compatibility (instead of the percent business).
 Problem is that when I looked for ways to get around braces "naturally"
 occurring in LaTeX, there weren't necessarily a lot of them.  (Ways, that
 is.)

 Oh, right. I just didn't see what in the code you were referring to. I see
 now.

 Anyway, to one of your earlier questions, with the new code I'm about to
 post the following conversions to and from Maxima work great:

 {{{
 sage: mb = maxima(bessel_I(1,x))
 sage: mb.sage()
 bessel_I(1, x)
 sage:  x,y = var('x,y')
 sage:  f = maxima(Bessel(typ='K')(x,y))
 sage: f.derivative('x')
 
%pi*csc(%pi*x)*('diff(bessel_i(-x,y),x,1)-'diff(bessel_i(x,y),x,1))/2-%pi*bessel_k(x,y)*cot(%pi*x)
 sage: m = f.derivative('x')
 sage: m.sage()
 -1/2*(x*bessel_I(-x, y)/y - x*bessel_I(x, y)/y + bessel_I(-x - 1, y) +
 bessel_I(x - 1, y))*pi*csc(pi*x) - pi*cot(pi*x)*bessel_K(x, y)
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4102#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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