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Results tagged with integration
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user 161318
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
7
votes
Is there a known closed form expression for this integral?
As you've pointed out, the only parameter that matters here is the angle $\theta$ between $x$ and $y$. To see how, consider instead the Gaussian integral:
$$
I(x,y)=\frac{1}{(2\pi)^{(d+1)/2}}\int_{u\i …
- 149
3
votes
1
answer
303
views
Application of Feynman parameters in an improper integral
I ask this because the above integral comes up in Bott-Taubes integration, and there is a lot of work done with respect to compactifying integration domains to make sure integrals are finite. …
- 149
2
votes
1
answer
221
views
Numerical computation of the second Vassiliev invariant, and the permutation $(1 3 4 2)$
$\DeclareMathOperator\SLL{SLL}$For a smooth embedding $\gamma(t):\mathbb{S}^1\rightarrow\mathbb{R}^3$, the Vassilev invariant of degree 2, which I will denote as $\nu_2(\gamma)$, may be computed numer …
- 149