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Show that $\sum_{n\le x} \mu ^2(n)=\frac{x}{\zeta(2)}+o(\sqrt{x}) \; (x\to \infty)$

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#analysis #number-theory #asymptotics #analytic-number-theory
71
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In which conditions $ f'(x)=O(g'(x))$ implies $f(x)=O(g(x))$?

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#derivatives #asymptotics
118
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Help me approximate this sum: $S = \sum_{j=2}^{N}{\frac{\ln \ln \ln \ j}{( \ln \ln \ j)^2}}$

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#integration #summation #asymptotics #approximation #approximate-integration
43
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Asymptotes and their like

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#asymptotics
1.6k
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Find witnesses proving that $f(x) = 2x^3 + x^2 + 5$ is $O(x^3 )$.

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#discrete-mathematics #asymptotics
292
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How can I prove $n - 2\sqrt{n} = \Theta(n)$

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#asymptotics
826
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Help with recurrence $T(n) = T(n/2) + n$

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#recurrence-relations #asymptotics #closed-form
136
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Monotone convergence of functions ant theor asymptotic power series

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#real-analysis #analysis #asymptotics #power-series #formal-power-series
57
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Unusual Asymptotics Question

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#asymptotics
305
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What are the bounds (upper and lower) for $|A+A|$?

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#elementary-set-theory #asymptotics #estimation #sumset
1.1k
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Euler-Maclaurin Summation

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#summation #asymptotics #euler-maclaurin
2.2k
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Find the asymptotic tight bound for $T(n)=T(n-1)+n lg n + n$ and for $T(n)=n^2 \sqrt{n}T(\sqrt{n})+n^5lg^3n+lg^5n$

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#algorithms #recurrence-relations #asymptotics #computational-complexity #recursive-algorithms
4.2k
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Slow decreasing function that exhibits asymptotic behaviour

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#calculus #asymptotics #special-functions
486
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An asymptotic expansion for $(1 + \frac{x}{n})^n$.

Published on
#asymptotics
65
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Big O notation - Asymptotics - Question

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#asymptotics

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