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I'm studying the asymptotic behavior (n -> infinity) of the following formula, where k is a given constant.

[tex]\frac{1}{n^{k (k + 1)/(2 n)}(2 k n - k (1 + k) \ln n)^2}[/tex]

I'm trying to do a series expansion on this equation to give the denominator a simpler form so that it is easier to make an asymptotic analysis.

I used mathematica/wolframalpha to expand the formula (the documents say Taylor expansion is used).

http://www.wolframalpha.com/input/?i=1/(n^(k+(k+++1)/(2+n))+(2+k+n+-+k+(1+++k)+Log[n])^2)

However in series expansion at n -> infinity, the result still has log n. This is actually a form I prefer, compared to the form [tex] a_0 + a_1 x + a_2 x^2 + ...[/tex] Does anyone see how the result is produced? Any help is much appreciated. Thanks.

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# Series expansion

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