New posts in Asymptotics

how to prove recursive function f(x) is in O(n)?

Conjecture: All but 21 non-square integers are the sum of a square and a prime

On Ramanujan's approximation, $n!\sim \sqrt{\pi}\big(\frac ne\big)^n\sqrt [6]{(2n)^3+(2n)^2+n+\frac 1{30}}$

Proof that $\pi =\lim_{n\to\infty}\frac{2^{4n}n!^4}{n(2n)!^2}$

Asymptotic behaviour of $\int_0^{\infty } x^{-x} \exp (n x) dx$

Asymptotic expansion of $\sum _{k=1}^n \left(\frac{k}{n}\right)^k$

Asymptotic expansion of $f(x)=\sum _{n=1}^{\infty } \frac{\sin \left(\sqrt{n}x\right)}{n}$ at the origin

Average decrease of a random number in "subtracting every prime by one in factorization"

Are there any divergent series that approximate to O(log log log n)?

Intuitive explanation of why some autonomous differential equations go to infinity in finite time