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Results tagged with asymptotics
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user 75422
Asymptotic behavior of functions, asymptotic series and related topics
0
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The Fransén-Robinson constant as a limit of integrals
This is the integral of the reciprocal gamma function,$$F=\int_0^\infty dx/\Gamma(x)= e+\int_0^\infty \frac{e^{-t}\ dt}{\log^2 t+\pi^2}$$ $$=e+\int_{-\infty}^{\infty}\frac{\exp(s-e^s)\ ds}{s^2+\pi^2}$ …
- 3,085
4
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Accepted
Upper limit function for the decay of $\int_x^\infty f(y)dy$, provided $f(y)$ is analytic, w...
$f(x):=\frac{\sin^2 x}{x^2}$ is entire, bounded on $\mathbb R$, and $\int_x^\infty f(y)\ dy$ decreases as $cx^{-1}$.
- 3,085
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Finding an asymptotic solution for a first order ODE
Not a full answer, but a hint at a negative answer: take $f(t)=\log t$, which doesn't satisfy $\lim_{t\to\infty}tf'(t)=\infty$, critically, but is nearer to the proven case (where $f'(t)=\omega(1)$ ). …
- 3,085