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Could somebody please explain spherical harmonics in a simpler manner than it is demonstrated on various websites (like the Wikipedia page which simply overflows my buffer with symbols). I've tried searching math.SE for some info on it, but it's mostly just used in explanations of other things. I'm familiar with calculus and spherical coordinates.

Some reasoning of why it came to be? How it works, etc.

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    See also: http://math.stackexchange.com/q/24671/53632012-04-03

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