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Asymptotic equation for $\sum_{k=1}^{n} \frac{\ln(k)^m}{k}$ for $m=1,2,3,4; n\gg0$?

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#sequences-and-series #logarithms #asymptotics
87
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Asymptotics of integral $ \int_{\delta}^{1}\frac{1}{\sqrt{y+e^{-y}-1}}~dy $

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#integration #sequences-and-series #analysis #asymptotics #improper-integrals
124
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Calculus with little $o$ notation

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#ordinary-differential-equations #asymptotics
120
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Solve Recurrence Equation: $T(n)=T(n−4)+n^2$

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#solution-verification #asymptotics #recurrence-relations
94
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Need help with this sum involving linear congruences

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#elementary-number-theory #summation #modular-arithmetic #asymptotics
60
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Looking for the sum an asympototic expansion of $\sum_{d|n}\frac{\Lambda \left({d}\right)}{d}$

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#number-theory #asymptotics
90
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Asymptotic expansion for reciprocal of Bessel function

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#sequences-and-series #asymptotics #power-series #divergent-series #bessel-functions
74
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Improper integral of vanishing functions

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#real-analysis #integration #limits #asymptotics #improper-integrals
72
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Let $f(x)$ be a non-negative decreasing function, goes to 0, what can we say about the asymptotic behaviour of $\sum_{p \leq x} f(p)$?

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#elementary-number-theory #prime-numbers #asymptotics #algebraic-number-theory #analytic-number-theory
95
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Show a function is in $L^2(\mathbb{R})$

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#real-analysis #functional-analysis #asymptotics #hilbert-spaces #improper-integrals
195
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Find estimates for the solution $x=x_n$ of the equation $(1+x)^n =1+(n+1)x$

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#calculus #inequality #asymptotics
118
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Hypergeometric Function near z = 1

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#asymptotics #power-series #hypergeometric-function
754
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Why is the time complexity of summing from 1 to n $O(n^2)$?

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#summation #asymptotics
68
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A question regarding fast-growing differentiable functions

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#derivatives #asymptotics
45
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What happens to $n$ in the Limit of some function...

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#limits #asymptotics #exponential-function

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