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Asymptotic behavior of integral $\int_1^\infty \frac{e^{-xt}}{\sqrt{1+t^2}}dt$ as $x \to 0$

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#real-analysis #asymptotics
99
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Give an example of a one-to-one function f(n) that is neither O(n) nor Ω(n) and justify it

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#analysis #algorithms #asymptotics #computer-science
303
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asymptotics of inverse Laplace transform of $\exp(\sqrt{s^3}-\sqrt{(s+1)^3})$

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#asymptotics #laplace-transform
104
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Analyze and find the solution Un in $u_k=u_{k−1}+k^2$ recurrence relation in terms of Big Theta

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#recurrence-relations #asymptotics
61
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Infinite series from 2 to k

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#summation #algorithms #asymptotics
40
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Suppose that $a_n=O(n)$ and $b_n=O(n^2)$. Let $c_n=a_n-b_n$

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#sequences-and-series #asymptotics
80
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Asymptotic behaviour of $\binom{n+\alpha-1}{n}$

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#complex-analysis #asymptotics #alternative-proof #gamma-function #binomial-theorem
52
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A bound for $x$ in an inequality.

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#inequality #asymptotics
329
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Why does (Sum from i=0 to lg(n) of 2^j) = (2n+1)?

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#discrete-mathematics #summation #asymptotics
8.2k
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Prove Big-Oh using Induction

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#discrete-mathematics #induction #asymptotics #factorial
72
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Compare functions

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#functions #discrete-mathematics #logarithms #asymptotics
133
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How to prove Asymptotic Theta Statement using ratios and l'hopital's rule?

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#limits #discrete-mathematics #asymptotics
133
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Prove or Disprove Big-Oh using ratio and limits

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#discrete-mathematics #asymptotics
820
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Proving an integral is finite

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#real-analysis #integration #asymptotics #estimation #bessel-functions
764
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Asymptotic notation (big O)

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#asymptotics

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