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Show that $u_n=\ln n + \frac{\ln n}{2n}+o\left(\frac{\ln n}{n}\right)$

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#real-analysis #asymptotics
64
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Asymptotic expansion of the series $\sum_{n=-\infty}^{\infty} \frac{\sin(\theta)}{-\cosh[(2n+1)\pi x] + \cos(\theta)}$

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#sequences-and-series #asymptotics
50
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Asymptotic normality of Kernel Density Estimator

Published on
#probability-theory #statistics #asymptotics
177
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uniformly continuous function on unbounded set

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#real-analysis #limits #continuity #asymptotics #uniform-continuity
45
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Equivalence in adaptive vs non-adaptive queries in complexity

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#asymptotics #computational-complexity #turing-machines
102
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Why is χ(G) NP-Hard and not NP-Complete

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#graph-theory #asymptotics #coloring
81
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Double pole problem in Mellin Transform

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#complex-analysis #asymptotics #complex-integration #mellin-transform
70
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Does $\log(f(x))\sim \log(g(x))$ implies $f(x)\sim g(x)$?

Published on
#limits #analysis #asymptotics
205
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Asymptotics of the sum $\sum_{k=1}^nn^{1/k}$ at $n\to\infty$

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#real-analysis #sequences-and-series #asymptotics
79
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Stirling's Formula for Quotient of Gamma Functions

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#asymptotics #gamma-function
14
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Limit of a function that contains a Bachmann–Landau term

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#limits #analysis #number-theory #asymptotics
110
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Asymptotics of $f(n)=\frac{2}{n}\sum_{i=1}^{n-2}f(i) + 1$

Published on
#limits #asymptotics #recurrence-relations
27
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On sufficients conditions for $f(x)=O(g(x))$ as $x\to \infty$

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#limits #analysis #asymptotics
97
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Why don't prime counting approximations work for Brocard's conjecture?

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#real-analysis #number-theory #asymptotics #conjectures
52
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Limit involving tail probability of multivariate normal

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#limits #asymptotics #normal-distribution #cumulative-distribution-functions

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