On Wednesday, April 16, 2014 3:34:25 PM UTC-4, Robert Dodier wrote:
>
> On 2014-04-16, kcrisman <[email protected] <javascript:>> wrote: 
>
> > (%i11) simplify_sum(sum(log(1-1/x^2),x,2,inf)); 
> >                                      inf + 2 
> > (%o11)                         log(-----------) 
> >                                    2 (inf + 1) 
> > 
> > Which I agree is not a great answer.  Using simpsum does the same thing. 
> >  I'm not sure if this is expected behavior in Maxima, though? 
>
> Well, %o11 is certainly incorrect, although it is perhaps not too 
> surprising. simplify_sum makes use of several methods, including 
> Gosper's and Zeilberger's methods, which (if I recall correctly) are 
> applicable to indefinite finite sums (i.e., upper limit is a symbol, 
> say m, such that m < inf). My guess is that such a method was 
> applied mistakenly to %i11. Of course, that's a bug in simplify_sum. 
>
>

 

> For the record: 
>
> (%i19) simplify_sum (sum (log (1 - 1/x^2), x, 2, m)); 
> (%o19) log((m+1)/(2*m)) 
> (%i20) limit (%, m, inf); 
> (%o20) -log(2) 
>

Thanks, Robert.  Yes, the latter is essentially why Jori's answer works, I 
believe. 

See http://trac.sagemath.org/ticket/16176 
and https://sourceforge.net/p/maxima/bugs/2722/

- kcrisman

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