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Results tagged with asymptotics
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user 80903
Asymptotic behavior of functions, asymptotic series and related topics
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161
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Asymptotics of certain sum with alternating sign (inclusion exclusion principle)
I would like to compute the asymptotics of the resulting sum $S$ when computing the number of possibilities to distribute $k$ indistinguishable objects in $m$ distinguishable boxes with size limitation … If I define the quasi-continuous variable $x=k/m$, I expect the asymptotics
\begin{align}
S_{m,R}(x)\sim \alpha p(m) e^{\beta m-\gamma(x-x_0)^2 m}\quad\text{as}\quad m\to\infty\,,
\end{align}
where $p( …
- 285
1
vote
Asymptotics of certain sum with alternating sign (inclusion exclusion principle)
The result is effectively derived in the reference for above. I overlooked this at first.
- 285