# Series expansion

1. May 17, 2013

### ELW

Hi,

I'm studying the asymptotic behavior (n -> infinity) of the following formula, where k is a given constant.
$$\frac{1}{n^{k (k + 1)/(2 n)}(2 k n - k (1 + k) \ln n)^2}$$

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 $$a_0 + a_1 x + a_2 x^2 + ...$$ Does anyone see how the result is produced? Any help is much appreciated. Thanks.

Last edited: May 17, 2013
2. May 20, 2013

### Stephen Tashi

I suggest that you post the result that your are talking about.