Hello, On Wednesday, February 23, 2011 5:25:45 AM UTC+1, Ronan Lamy wrote: > > The conventional definition of the order of the expansion is that it's > the degree of the last term included in the polynomial approximation, so > one less than the order of the excluded terms. Your example is a > second-order expansion, because it gives a second-order approximation. > I agree up to a small detail. I think the usual way is to write e.g. f(x) = cos(x) as f(x) = 1 - 0.5 x^2 + O(4). Note the O(4) term. I think this is usually done to reflect the fact that in this expansion cannot contain uneven powers of x as cos(x) is an even function. Though competitors such as Mathematica are not that smart, I think a behaviour like this might be worth considering.
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