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$\sum_{k=0}^{n}p_{2k+1}-p_{2k} \sim f(n)$

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#number-theory #prime-numbers #asymptotics #prime-gaps
80
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Does this BVP have an analytic solution?

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#ordinary-differential-equations #asymptotics #boundary-value-problem #eigenfunctions
62
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Computing $\text{lim}_{n \rightarrow \infty}\frac{n!}{n^{\lfloor y\sqrt{n} \rfloor}(n-\lfloor y \sqrt{n}\rfloor)!}$

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#calculus #limits #asymptotics
40
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Asymptotic evaluations of a limit: $\lim_{x\to 0}\frac{\ln(1+x^3\cos 3x)}{2x^3(1-\sqrt{1+\cos 3x)}}$

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#calculus #limits #asymptotics #limits-without-lhopital
15
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Why is $ |x-\mu|^\alpha+|x-\mu|^n=\Theta(|x|^n)$ at $x \to \infty$?

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#limits #asymptotics
357
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Does a function have multiple Big-$O$'s?

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#limits #asymptotics #definition
59
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Asymptotic for $\int_0^1 z e^{-\frac{(d+z)^2}{a}} \text d z$ for $a\to 0$.

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#integration #asymptotics
94
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Asymptotic dominance analysis

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#real-analysis #sequences-and-series #asymptotics #self-learning
274
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Prove Big O notation with log

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#asymptotics
86
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Number of ways of writing $m=m_1\cdots m_k$

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#number-theory #asymptotics #analytic-number-theory #factoring
2.6k
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Intuitive explanation of why some autonomous differential equations go to infinity in finite time

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#ordinary-differential-equations #asymptotics #infinity #singularity
45
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Solving a difficult equation involves both factorial and non-square root

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#logarithms #asymptotics #exponential-function #factorial #fractions
62
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Asymptotic behavior (big O) of a function involving a nonsolvable integral

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#calculus #asymptotics
33
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Problem in defining the initial conditions for asymtotic expansion (Heat Equation)

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#partial-differential-equations #asymptotics #heat-equation #perturbation-theory
108
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Asymptote for $\frac{\left(\Gamma(1+1/t)\right)^2}{\Gamma(1+2/t)}$

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#calculus #integration #definite-integrals #asymptotics #upper-lower-bounds

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