On Tuesday, 19 January 2016 17:22:52 UTC, kcrisman wrote:
>
>
>> As Dima mentions, the relevant functionality is coming from Maxima in 
>> this case. Maxima does have a flag you can set to let it try to expand 
>> bessel functions into elementary functions, see 
>> http://maxima.sourceforge.net/docs/manual/maxima_15.html#SEC80
>>  It's not directly exposed in sage, but with some obscure code you can 
>> activate it:
>>
>> sage: maxima_calculus("besselexpand:true")
>> true
>> sage: sum(((-1)^n)*((x)^(2*n+1))/factorial(2*n+1),n,0,oo)
>> sin(x)
>>  
>>
>
> Thanks, Nils.  As usual, the question becomes whether this should 
> "automagically" happen in Sage for certain simplifications...
>

perhaps a part of simplify_full() ?
 

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