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Adding to the for dummies.

The real spherical harmonics are orthonormal basis functions on the surface of a sphere.

I'd like to fully understand that sentence and what it means.

Still grappling with

  • Orthonormal basis functions (I believe this is like Fourier Transform's basis functions are sines and cosines, and sin is orthogonal to cos, and so the components can have a zero inner product..)
  • ".. are orthonormal basis functions ..on the surface of a sphere".
    • What sphere? Where does the sphere come from? Do you mean for each position on the sphere, we have a value? Is the periodicity in space on the sphere exploited? Is that how we get the higher order terms?
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    Did you read the wikipedia page? http://en.wikipedia.org/wiki/Spherical_harmonics2011-03-02
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    Yes. That wiki page is pretty opaque to me at the moment.2011-03-02
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    A "function on X" is generally a function from X to R. So a function on the surface of a sphere is a function from, say, {(x, y, z) : x^2 + y^2 + z^2 = 1} to R. (I'm not sure what "what sphere" means.)2011-03-02
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    @bobobobo, you may be interested in the recent book: http://www.amazon.com/Applications-Fractional-Calculus-Physics-Hilfer/dp/98102345702013-01-16

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