Newbetuts

Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$

Ratio of $2$-norm to infinity norm of coefficients in the expansion of $(1+𝑥+𝑥^2+\ldots+x^m)^n$?

Number of distinct prime divisors of an integer $n$ is $O(\log n/\log\log n)$

How do I prove that $2^n=O(n!)$?

Asymptotic behaviour of sum over the inverse japanese symbol

How do I prove $\sum_{n \leq x} \frac{\mu (n)}{n} \log^2{\frac{x}{n}}=2\log{x}+O(1)$? Can I use Abel summation?

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

Find asymptotic of recurrence sequence

Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$

How many numbers $n$ are there such that $\gcd(n,\phi(n)) = 1$?

How to compute the asymptotic growth of $\binom{n}{\log n}$?

Variations on the Stirling's formula for $\Gamma(z)$

Estimate $\displaystyle\int_0^\infty\frac{t^n}{n!}e^{-e^t}dt$ accurately.

Asymptotic Expansion of the Bessel-Integral Function

What is the mistake in my derivation of the wrong asymptotic relation $n^n = O(n!)$?

Good upper bound for $\sum\limits_{i=1}^{k}{n \choose i}$?

New posts in asymptotics

Asymptotics of inverse of normal CDF

Asymptotic behaviour of $\sum_{p\leq x} \frac{1}{p^2}$

How to recognise intuitively which functions grow faster asymptotically?

Reworking $\sum_{n \leq x} \frac{1}{n^s}$, where $n$ is relatively prime to some fixed $k$

Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$

Ratio of $2$-norm to infinity norm of coefficients in the expansion of $(1+𝑥+𝑥^2+\ldots+x^m)^n$?

Number of distinct prime divisors of an integer $n$ is $O(\log n/\log\log n)$

How do I prove that $2^n=O(n!)$?

Asymptotic behaviour of sum over the inverse japanese symbol

How do I prove $\sum_{n \leq x} \frac{\mu (n)}{n} \log^2{\frac{x}{n}}=2\log{x}+O(1)$? Can I use Abel summation?

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

Find asymptotic of recurrence sequence

Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$

How many numbers $n$ are there such that $\gcd(n,\phi(n)) = 1$?

How to compute the asymptotic growth of $\binom{n}{\log n}$?

Variations on the Stirling's formula for $\Gamma(z)$

Estimate $\displaystyle\int_0^\infty\frac{t^n}{n!}e^{-e^t}dt$ accurately.

Asymptotic Expansion of the Bessel-Integral Function

What is the mistake in my derivation of the wrong asymptotic relation $n^n = O(n!)$?

Good upper bound for $\sum\limits_{i=1}^{k}{n \choose i}$?