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Big O of multiple variables

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#asymptotics #computational-complexity
46
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Volume of the unit sphere converges to $0$ faster than any $a_n := a^n$ with $0<a<1$.

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#calculus #limits #asymptotics
1.3k
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Is there a parabola which is similar to a branch of hyperbola?

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#asymptotics #conic-sections #coordinate-systems
1.9k
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For sufficiently large $n$, Which number is bigger, $2^n$ or $n^{1000}$?

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#real-analysis #sequences-and-series #number-theory #inequality #asymptotics
97
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Probability of being in same connected component

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#probability #combinatorics #graph-theory #asymptotics #random-graphs
840
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Why Is This Algorithm Not In Polynomial Time?

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#algorithms #asymptotics #computational-complexity
159
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A bridge between the sum of the divisors and the Totient function

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#number-theory #asymptotics #totient-function #divisor-sum
299
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Asymptotic distribution of Gini's mean difference

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#statistics #asymptotics #statistical-inference
512
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What is the rate of growth of $M_n := \max_{1 \le i \le n} U_i^{(n)}$, where $U_i^{(n)} \sim \operatorname{Uniform}[0,n]$? Is it "constant"?

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#probability-theory #asymptotics #probability-limit-theorems #order-statistics #upper-lower-bounds
234
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WKB Approximation to Schrödinger Equation

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#ordinary-differential-equations #numerical-methods #asymptotics #wave-equation #perturbation-theory
358
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Domain of validity for the asymptotic expansion of the Bessel function of the first kind

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#asymptotics #bessel-functions
3.2k
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What proportion of positive integers have two factors that differ by 1?

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#number-theory #asymptotics
57
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Given $f(x)=o(1), g(x)=O(h(x)) \text{ as } x\to a $, show that $f(x)g(x)=o(h(x))$

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#calculus #limits #discrete-mathematics #asymptotics
44
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Why this time complexity is not a valid answer?

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#algorithms #asymptotics
32
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Does bounded version of Lagrange's 4-square theorem follow from this result?

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#number-theory #proof-verification #asymptotics #sums-of-squares

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