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Results tagged with asymptotics
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user 37555
Asymptotic behavior of functions, asymptotic series and related topics
3
votes
Accepted
How to estimate a summation?
Put $a=|v_1|$, $b=|v_2|$, $c=|v_1v_2|$. Then we have
$$
\sum_{i=0}^a\sum_{j=0}^b\sum_{k=0}^c\binom{a-c}{i-k}\binom{b-c}{j-k}= \sum_{k=0}^c\left(\sum_{i=0}^a\binom{a-c}{i-k}\right)\left(\sum_{j=0}^b\bi …
3
votes
Getting asymptotic behaviour of an integral?
If you need better asymptotics, you would have to use the series expansion of $\frac{1}{1+x}$. …
3
votes
Asymptotics of a recursion
The first factor telescopes completely, and the second becomes easier by combining $\alpha_{2\kappa}$ with $\beta_{2\kappa+2}$, so
$$
c_{2k} = \frac{1+\ell}{(2k-1)(2+\ell)}\prod_{\kappa=1}^k \left(1-\ …
2
votes
Accepted
Bombieri-Vinogradov in short intervals
As far as I know the Prime Number Theorem in the form $\pi(x+x^\theta)-\pi(x)\sim\frac{x^\theta}{\log x}$ is not proven for any fixed $\theta<\frac{7}{12}$. So I guess the best you could hope for woul …