# Questions tagged [asymptotics]

For questions involving asymptotic analysis, including function growth, Big-$O$, Big-$\Omega$ and Big-$\Theta$ notations.

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### Find all $\alpha, \beta, \gamma$ such that $(C_{2^n}^n)^{\frac1n}\sim\alpha n^{\beta} \gamma^{n}$

I'd like to get some help in solution of the following task: Find all real $\alpha, \beta, \gamma$ such that $(C_{2^n}^n)^{\frac1n}\sim\alpha n^{\beta} \gamma^{n}$ I've found that the left part is ...
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### Finding constant for asymptotic equality

I have the following task and I'd like you to check my thoughts on it: Is there a constant C such that when $n \to \infty$ it is true that $\frac{(2n)!}{n!n^n} = (C + o(1))^n$ If such constant C ...
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### Consequence related to Bollobas' theorem about chromatic number of a random graph

I've came across the following theorem: let $G(n,p)$ be a random graph and let $p = p(n) = n^{-\alpha}, \alpha \in (\frac{1}{2}, 1)$ then there is a function $u=u(n, \alpha)$ such that asymptotically ...
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### How to find $\delta$ such that the formula growth with n [closed]

How to write the lowest $\delta(n)\in(0,1)$ we can get such that $$\frac{n^2\delta^2(1-2p)^2}{p(1-p)}$$ tends to infinity when n tends to infinity? Here $p$ is a function on $n$ that approaches $1/2$ ...
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### On the order of growth of entire functions

Definition. Let $f: \mathbb{C} \to \mathbb{C}$ be an entire function. The order of growth of $f$, denoted by $O_G(f)$, is defined as O_G(f) := \inf \left\{r > 0: \exists A, B &...
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