Taylor Series and Asymptotic Expansions
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چکیده
There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(x) as n → ∞.
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