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Using $\ln x<(x^\epsilon-1)/\epsilon$ for $x>1$ and $\epsilon>0$, and the squeeze theorem, show that $\lim\limits_{x\to\infty}(\ln x)/x^\epsilon=0$

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#real-analysis #asymptotics
67
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Maximum of uniformal idd random variables involving the Gamma function

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#probability #random-variables #asymptotics #gamma-function
32
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Convergence rate for recurrence relation $u_{k+1} \le \left(1- \frac{c}{k}\right) u_k + \frac d {k^2}$

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#sequences-and-series #recurrence-relations #asymptotics
67
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Asymptotic notation proof

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#asymptotics #computational-mathematics
118
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How do you derive an equation if you know the asymptotes?

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#calculus #linear-algebra #asymptotics #algebraic-curves
458
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Coefficients of the stirling's series expansion for the factorial.

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#sequences-and-series #asymptotics #power-series #factorial #gamma-function
75
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Asymptotic behavior of zeroes of $\ln(t)-t+n$

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#calculus #sequences-and-series #limits #logarithms #asymptotics
620
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Asymptotic expansion of the hypergeometric function

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#asymptotics #special-functions #hypergeometric-function
37
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Series for roots

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#asymptotics
115
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Equivalent definitions of $X_n = O_p(1)$

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#probability-theory #statistics #convergence-divergence #asymptotics
57
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Who is known before : Asymptotic expansion or factorial notion?

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#asymptotics #taylor-expansion #factorial #math-history
1.7k
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Big O - Prove that the sum $\sum_{i=1}^n i^2 = O(n^3)$

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#summation #asymptotics
348
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Asymptotics of a recursive sequence

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#real-analysis #combinatorics #complex-analysis #asymptotics #generating-functions
167
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Estimate convergence order of a sequence

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#sequences-and-series #asymptotics #rate-of-convergence
152
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Find all asymptotes of given curve

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#asymptotics #algebraic-curves

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