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Approximation of $\left(1-\frac{k}{n}\right)^{k}$ where $k=o(\sqrt{n})$

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#combinatorics #limits #asymptotics #computational-complexity
69
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Characterize $\frac {ax + b} {cx + d}$ as $x \to \frac {-d} c$

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#calculus #asymptotics #rational-functions
69
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How to prove $\sum_{k=n}^{\infty}\frac{1}{k^2}=O(\frac{1}{n})$?

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#real-analysis #sequences-and-series #analysis #inequality #asymptotics
114
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How can $(\ln n)^4 < n$?

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#limits #logarithms #asymptotics
35
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$O(\ln(\ln n))$ rounds to achieve $(\ln n)^4$ players

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#logarithms #asymptotics
69
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Erdos-Lehner theorem for partition function of different parts

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#combinatorics #asymptotics #integer-partitions
112
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Generalization of Laplace's method

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#real-analysis #integration #asymptotics
122
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Two Definitions of Big-O notation when Doing Addition?

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#analysis #proof-explanation #asymptotics
44
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proof for small o order relation with big o and omega.

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#algorithms #proof-explanation #asymptotics
143
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Asymptotics for $f(x)$ such that $f(x) + f(x/2) + f(x/3) + f(x/4) + ... = x$?

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#number-theory #prime-numbers #asymptotics #functional-equations #functional-inequalities
175
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Calculus with little-o notation: Follow-up

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#ordinary-differential-equations #asymptotics
105
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Asymptotic behavior of solution to a nonlinear ode.

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#real-analysis #analysis #asymptotics #stability-in-odes
40
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Asymptotic behavior of n-th derivatives at 0 of a solution to a differential equation

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#real-analysis #ordinary-differential-equations #asymptotics
111
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Does the norm of the sum of $n$ 2d random vectors also scale as $\sqrt{n}$?

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#geometry #probability-theory #asymptotics #normal-distribution #expected-value
99
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Evaluation sum and its asymptote $\sum_{s=1}^{N} \sum_{t=1}^{N} \left[{\sqrt{4t-s^2} \in \mathbb{Z}}\right]$

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#elementary-number-theory #summation #asymptotics #square-numbers

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