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Results tagged with integral-transforms
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user 32389
For questions about integral transforms, inlcuding the Fourier transform, Laplace transform, Radon transform, Mellin transform, Hankel transform etc.
4
votes
Numerically computing $\int_0^1 \frac{1}{\sqrt{1-x^4}}dx$
How Gauss (supposedly) calculated this integral in terms of AGM (namely $M(1,\sqrt{2})$) is outlined in http://home.sandiego.edu/~langton/gaussagm.pdf (Gauss, recurrence relations, and the AGM, by Sta …
- 16.5k
10
votes
volume over a hypercube, over simplex: twist by Euler numbers
This is only a partial answer. The Beukers-Kolk-Calabi change of variables
$$x_1=\frac{\sin{u_1}}{\cos{u_2}},\;\;x_2=\frac{\sin{u_2}}{\cos{u_3}},\ldots,
\;x_{n-1}=\frac{\sin{u_{n-1}}}{\cos{u_n}},\;\;x …
- 16.5k