List questions from asymptotics

168

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

Published on 26 Jan 2018 - 15:53

61

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Maximum of uniformal idd random variables involving the Gamma function

Published on 26 Jan 2018 - 16:42

26

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Convergence rate for recurrence relation $u_{k+1} \le \left(1- \frac{c}{k}\right) u_k + \frac d {k^2}$

Published on 26 Jan 2018 - 21:58

58

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Asymptotic notation proof

Published on 22 Mar 2026 - 9:21

114

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How do you derive an equation if you know the asymptotes?

Published on 17 Mar 2026 - 16:18

453

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Coefficients of the stirling's series expansion for the factorial.

Published on 24 Mar 2026 - 23:48

72

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Asymptotic behavior of zeroes of $\ln(t)-t+n$

Published on 27 Jan 2018 - 23:43

611

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Asymptotic expansion of the hypergeometric function

Published on 22 Mar 2026 - 5:02

32

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Series for roots

Published on 28 Jan 2018 - 12:16

111

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Equivalent definitions of $X_n = O_p(1)$

Published on 28 Jan 2018 - 13:05

52

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Who is known before : Asymptotic expansion or factorial notion?

Published on 24 Mar 2026 - 23:46

1.7k

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Big O - Prove that the sum $\sum_{i=1}^n i^2 = O(n^3)$

Published on 28 Jan 2018 - 21:04

342

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Asymptotics of a recursive sequence

Published on 22 Mar 2026 - 12:27

157

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Estimate convergence order of a sequence

Published on 22 Mar 2026 - 2:37

147

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Find all asymptotes of given curve

Published on 17 Mar 2026 - 1:30

List Question

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

Maximum of uniformal idd random variables involving the Gamma function

Convergence rate for recurrence relation $u_{k+1} \le \left(1- \frac{c}{k}\right) u_k + \frac d {k^2}$

Asymptotic notation proof

How do you derive an equation if you know the asymptotes?

Coefficients of the stirling's series expansion for the factorial.

Asymptotic behavior of zeroes of $\ln(t)-t+n$

Asymptotic expansion of the hypergeometric function

Series for roots

Equivalent definitions of $X_n = O_p(1)$

Who is known before : Asymptotic expansion or factorial notion?

Big O - Prove that the sum $\sum_{i=1}^n i^2 = O(n^3)$

Asymptotics of a recursive sequence

Estimate convergence order of a sequence

Find all asymptotes of given curve

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