>>>>> "Mike" == Mike Valenzuela <mickle.mouse at gmail.com> writes:
Mike> I was just wondering if there was a more comprehensive
Mike> function than nusum. I have noticed that nusum fails to
Mike> convert back many power series. Although maybe this is on
Mike> purpose as power series are not always guaranteed to
Mike> converge to the function they come from?
Mike> I'm looking for something like "unpowerseries" (perhaps
Mike> using some simple processing followed by a lookup table, or
Mike> some method similar to how maxima does integration).
Mike> The expected behavior I would like from such a function can
Mike> be demonstrated as:
Mike> (i1): unpowerseries( sum( exp(t*k) * lambda^(-k) * exp(-lambda) / k! )
Maybe simplify_sum will do what you want:
load(simplify_sum);
simplify_sum(sum( exp(t*k) * lambda^(-k) * exp(-lambda) / k!, k, 0, inf))
-> %e^(%e^t/lambda-lambda)
Ray