On 2014-04-16, kcrisman <
kcri...@gmail.com> 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)
best,
Robert Dodier