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Results tagged with asymptotics
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user 21724
Asymptotic behavior of functions, asymptotic series and related topics
5
votes
Accepted
Cardinality of growth rates
Let me rather define $f=o(g)$ as $\forall \varepsilon > 0, \exists x_0, \forall x \geq x_0, |f(x)| \leq \varepsilon |g(x)|$.
Let $f_0,f_1$ be such that $f_0 = o(f_1)$. Let us assume that we have a f …
- 7,249
9
votes
Accepted
Asymptotic estimate of double summation
Using the decomposition
$$
H(x) := \sum_{a \leq x} \frac{1}{a} = \log(x) + \gamma - \frac{\psi(x)}{x} + \int_{x}^{+\infty} \frac{\psi(t) d t}{t^2},
$$
where $\psi(t) = \{ t \} - \frac{1}{2}$, one ge …
- 7,249