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Results tagged with asymptotics
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user 118090
Asymptotic behavior of functions, asymptotic series and related topics
5
votes
1
answer
292
views
Asymptotic of integral $\int_{1}^{e^n}(1-\frac{\ln(x)}{n})^n\,dx$
How could we find the large-$n$ asymptotic of $$\int_{1}^{e^n}\left(1-\frac{\ln x}{n}\right)^n\,dx.$$
I have a suspicion that this is $\sqrt{n}$.
-2
votes
2
answers
461
views
Lower bound of q pochhammer symbol [closed]
How one could prove, that q pochhammer symbol $(1,1/n) = \prod_{k = 1}^{\infty}(1-\frac{1}{n^k}) \geq 1 - \frac{1}{n-1}$