Roots 1977 DVDRip X264 AC3 Gopo EP1-6
公開日:2022/06/22 / 最終更新日:2022/06/22
Roots 1977 DVDRip X264 AC3 Gopo EP1-6
Download ::: https://tinurll.com/2sd893
Roots 1977 DVDRip X264 AC3 Gopo EP1-6
Sounds like good work done.
. -gopo-ep1-6
Q:
Spherical harmonics basis
I need a basis of spherical harmonics on a sphere. From what I’ve read, we have
$$
\frac{\mathbf{e}^{\mathbf{m}}}{\sqrt{2\pi}^3}Y_{\mathbf{m}}(\theta,\phi)
$$
where $\mathbf{e}^{\mathbf{m}}$ is a vector, $\theta$ is an angle in the radial and $\phi$ is an angle in the azimuthal directions (two angles).
This implies that $Y_{\mathbf{m}}(\theta,\phi)$ is a vector, i.e., two angles. I know it has six components, and I’m having a bit of trouble with this point.
A first try could be to expand the vector $\mathbf{e}^{\mathbf{m}}$ in the spherical harmonics
$$
\mathbf{e}^{\mathbf{m}}=\sum_{\mathbf{n}}c_{\mathbf{n}}\mathbf{Y}_{\mathbf{n}}
$$
and then compute
$$
\frac{\mathbf{e}^{\mathbf{m}}}{\sqrt{2\pi}^3}Y_{\mathbf{m}}(\theta,\phi)=\frac{1}{\sqrt{2\pi}^3}\sum_{\mathbf{n}}c_{\mathbf{n}}Y_{\mathbf{n}}(\theta,\phi)
$$
Then $\mathbf{n}$ and $\mathbf{m}$ are equivalent (I’m not sure if this is true, but is is fine for this problem).
Now, if I compute $Y_{\mathbf{n}}(\theta,\phi)$ with the above expansion, do I get the right set of basis functions for spherical harmonics? If not, what are the equations to generate this set?
Edit: I’m not sure about this, so I’ll ask a second question, just to make sure: the above is just an expansion in spherical harmonics, right?
A:
The basic spherical
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