23.02.2011 16:27, Alexander Eberspächer пишет:
cos(x) as
f(x) = 1 - 0.5 x2 + 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
Formally, this variant do not reflect anything about even or odd terms
knowlage. It only reflect that some zeros terms intellectually
discovered: from 3 order (what precision was required) continually up to
some term (x^4) that founded as non zero.
Well, suppose this variant further with comparison of present.
First of all, can I be curious about another practical aims of this?
For example, present variant is can be used for this (for me):
"Give me terms only that is required for me, I do not want to know
unnecessary information and deal with it. Also, when I begin with some
asymptotic expansion with some precision, and then continue to work with
series (summation, multiplication and various operations) inform me the
finally (guaranteed) precision"
Your variant may be of course useful on some topics, but obviously it
produce some investigation about terms of series. So my conclusion is to
shape this variant logically separately. (f.e. as options of method, or
another method, or something else).
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