Comment #5 on issue 2723 by asmeurer: What should summation() do with
non-integer limits?
http://code.google.com/p/sympy/issues/detail?id=2723
I just noticed that the result sympy gives is the same as the one you want,
except at the point a = 0, where it's the same if you take the limit.
To see this, do
In [41]: c = summation(exp(a*x), (x, -S(1)/2, S(1)/2))
In [42]: expand(cancel(c.subs(exp(a/2), x)))
Out[42]:
1
x + ─
x
In [43]: expand(cancel(c.subs(exp(a/2), x))).subs(x, exp(a/2))
Out[43]:
a -a
─ ──
2 2
ℯ + ℯ
So the issue really isn't as bad is it originally seemed. Unfortunately,
cancel() is not smart enough currently to do something like the above
automatically (this should be a new issue).
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