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Asymptotic relations at infinity

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#asymptotics
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What is the limit inferior of $p_n^2/ (\log p_n) \left\lvert 1-e^\gamma\log(p_n+\log^2p_n+\varepsilon_n)\prod_1^n (1-1/p_k)\right\rvert$?

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#real-analysis #number-theory #limits #prime-numbers #asymptotics
212
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Estimating the number of permutations with no increasing subsequences of a prescribed length

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#probability #combinatorics #asymptotics
78
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Prove that $1^3 + 2^3 + \cdots+n^3$ is $O(n^4)$

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#discrete-mathematics #asymptotics
441
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What is known about the counting function of Gaussian primes"

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#prime-numbers #asymptotics #gaussian-integers
536
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Averaged Multinomial Coefficient

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#asymptotics #multinomial-coefficients
1.1k
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Does any quadratic function in the form $an^2 + bn + c$ equal $\Theta(n^2)$ in asymptotic notation?

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#asymptotics #quadratics
106
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$\prod _{k=2}^{n} {\log k}$ is big-$O$ of what?

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#real-analysis #asymptotics #computer-science
76
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What's about $\sum_{k=1}^{n-1} p_{k} \sum_{l=k+1}^{n} p_{l}$ for prime numbers?

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#sequences-and-series #prime-numbers #asymptotics #analytic-number-theory
43
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Running Time Analysis

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#asymptotics #computer-science
321
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Proportion of elements of prime order $p$ in $S_n$

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#group-theory #number-theory #prime-numbers #asymptotics #symmetric-groups
7.7k
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Complexity of FFT algorithms (Cooley-Tukey, Bluestein, Prime-factor)

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#asymptotics #computational-complexity #fourier-transform #fast-fourier-transform
5.7k
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Arrange the following:$(1.5)^n, n^{100}, (\log n)^3, \sqrt n\log n, 10^n, (n!)^2, n^{99}+n^{98}, 101^{16}$

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#asymptotics #computer-science
268
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$2\times 2$ block Toeplitz determinant

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#matrices #asymptotics #determinant #block-matrices
150
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Big-O proof of inclusion

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#algorithms #asymptotics

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