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First order taylor expansion formal proof

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#asymptotics #finite-differences #pattern-recognition
38
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Rate of growth of a modified series

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#real-analysis #sequences-and-series #analysis #asymptotics #estimation
39
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If $\sum_{i =1}^ja_i$ is divergent and $a_n \sim f(n)$, is it true that $\lim_{k \to \infty}\sum_{i =1}^ka_i = \lim_{k \to \infty}\sum_{i =1}^kf(i)$?

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#sequences-and-series #limits #proof-verification #asymptotics
498
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estimating the tail of $p$-series

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#sequences-and-series #analysis #asymptotics #divergent-series
88
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Trouble understanding how a big-o bound proves a limit

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#number-theory #limits #asymptotics
139
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Positive real solution to $x^n=x+1$

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#asymptotics #roots #inverse #approximation
136
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Asymptotic equivalence and lim inf, lim sup

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#asymptotics #limsup-and-liminf
384
Views

How does $a^{a^n}$ compare with $n!$ asymptotically?

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#algorithms #asymptotics #exponentiation #factorial
59
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Asymptotic integral with bessel function

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#asymptotics #contour-integration #bessel-functions
65
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Sufficient conditions for $\lim_{N \to \infty} \frac{{_2 F_1} (a,b;c+N;z)}{{_2 F_1} (a,b;c+N+1;z)}=1$

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#asymptotics #hypergeometric-function
282
Views

Asymptotic behaviour of $f(x) = \sum_{n=1}^\infty n^\varepsilon \frac{x^n}{n!}$ for $\varepsilon\in(0,1)$

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#asymptotics #power-series #exponential-function #analytic-functions
52
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Asymptotic behaviour of $\frac{1}{2\pi^2|\vec{x}-\vec{x}_0|}\int_0^{\infty}dp~ p \sin(p|\vec{x}-\vec{x}_0|)e^{-it\sqrt{p^2+m^2}}$ for $x^2\gg t^2$

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#integration #complex-analysis #asymptotics #physics #stationary-point
482
Views

Asymptotic value of Meijer G-function

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#asymptotics #residue-calculus #hypergeometric-function
78
Views

Prove that a certain series grows as $O(\log n)$

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#real-analysis #sequences-and-series #asymptotics #upper-lower-bounds
34
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Can we get a polynomial time algorithm from a naively exponential one, because of a linear formula that's bounded?

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#inequality #algorithms #asymptotics #computer-science #computational-complexity

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