Tagged Questions
2
votes
2answers
45 views
Prove the following: Product of Roots
$1^{(1/1)} \cdot 2^{(1/2)} \cdot 3^{(1/3)} \cdot 4^{(1/4)} \cdot 5^{(1/5)} $.... diverges
well I don't really know if it does but my gut tells me it does:
I can take the log of this product
to ...
1
vote
0answers
75 views
Asymptotics of an integral
Consider an integral
$$
I(x) = \int\limits_{\mathbb{R}^n} e^{i\xi x } \delta(\xi^2-k^2)\chi( (\xi-k,\gamma)) \, d\xi
$$
where $x, k, \gamma \in \mathbb{R}^n$, $|\gamma| = 1$ and $(x,y)\equiv xy = ...
2
votes
1answer
103 views
Asymptotics of an improper integral
I have to show that if $x \to \infty$, then
$$
\int\limits_{\mathbb{R}^d} \frac{e^{i\xi x}}{\xi^2 + 2k\xi}d\xi = O\left(|x|^{-\frac{d-1}{2}} \right) \;\;\; \; d\geqslant2, \;\;\; k\in \mathbb{C}^d
...
