List questions from asymptotics

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Show Time $T(n) = Θ(n^3)$

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Obtaining the Airy kernel from the Christoffel-Darboux formula with asymptotic Hermite polynomials

Published on 14 Apr 2026 - 3:30

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Lommel function

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how to find the asymptotic expansion of the following sum:

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Expected length of the shortest polygonal path connecting random points

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Speed of convergence of Riemann sums

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Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$?

Published on 14 Apr 2026 - 11:33

108

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asymptotic approximation when $a\to 0^+$ of $I(a):=\int_0^\infty \int_0^{a/x}e^{-x-y}\ dy\ dx.$

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Asymptotic behavior of $\sum_{n>x} \frac{\log n}{n^2}$

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Derivative of big O symbol

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Show $f(x) = (x^4+x^2+1)/(x^3+1) $ is $O(x)$

Published on 17 Apr 2026 - 2:54

656

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How to evaluate $\sum\limits_{k=0}^{n} \sqrt{\binom{n}{k}} $

Published on 12 Apr 2026 - 11:27

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Does $ \log(x)^{x^a}$ eventually dominate $x^k$?

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Asymptotics of logarithms of functions

Published on 12 Apr 2026 - 2:55

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Help understanding solution to growth of partition function

Show Time $T(n) = Θ(n^3)$

Obtaining the Airy kernel from the Christoffel-Darboux formula with asymptotic Hermite polynomials

Lommel function

how to find the asymptotic expansion of the following sum:

Expected length of the shortest polygonal path connecting random points

Speed of convergence of Riemann sums

Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$?

asymptotic approximation when $a\to 0^+$ of $I(a):=\int_0^\infty \int_0^{a/x}e^{-x-y}\ dy\ dx.$

Asymptotic behavior of $\sum_{n>x} \frac{\log n}{n^2}$

Derivative of big O symbol

Show $f(x) = (x^4+x^2+1)/(x^3+1) $ is $O(x)$

How to evaluate $\sum\limits_{k=0}^{n} \sqrt{\binom{n}{k}} $

Does $ \log(x)^{x^a}$ eventually dominate $x^k$?

Asymptotics of logarithms of functions

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