Roots 1977 DVDRip X264 AC3 Gopo EP1-6 HOT!

Roots 1977 DVDRip X264 AC3 Gopo EP1-6 HOT!

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Roots 1977 DVDRip X264 AC3 Gopo EP1-6

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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

SOV. WVOS, Radio Station

Vincent Ressal, WVOS, “Wind River”, 25 August 1952

WVOS, Radio Station, is located at 2410 North Greenwich Street in Grand
Rapids, Michigan. The transmitter site is at the top of the radio tower.
The antenna is an FM directional Yagi with 5 radials. WVOS, Radio Station, is
an AM sister station of WMRD, Radio Station, and has a 100,000 watt signal.

This recording, “Wind River,” was recorded on 7 August 1952. The high
frequency of the audio in this recording has been magnified, by the
magnifying button to the right of the YouTube window, to better hear the
sound quality. The recording only has a 1.7 second clip, because there is a
slight chirp in the beginning. Because this recording is 2 ½ minutes long,
the opening and closing shows of the recording and the credit roll, have
been removed.

Paul Poteet, WVOS, “Wind River,” 7 August 1952

Vincent Ressal, WVOS, “Wind River,” 25 August 1952

References

Further reading

External links
History of the station: 910 FM

Category:Radio stations in Michigan
Category:Radio stations established in 1961
Category:Grand Rapids, Michigan
VOS
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