> what level of math do I need to understand this?
A basic understanding of differential equations is all that's really necessary, but knowing about orthogonal polynomials would be helpful too.
> something I can catch up on in a weekend?
Probably not. If you know any calculus (even a basic high school class should be enough), two weekends would probably be enough; if you don't know calculus, then double it.
My advice would be to use an introductory level quantum physics textbook or an advanced chemistry textbook, since the spherical harmonics are used quite a bit in those fields. You could use a math textbook too, but those will tend to focus on details that are irrelevant to you.
An alternate path would be to learn about Fourier series/transformations, then what's discussed in the article will follow as a natural consequence. This is probably a harder option, but there's lots of really good learning materials online for Fourier transformations (and comparatively little for spherical harmonics), so it may end up being easier for you.
A basic understanding of differential equations is all that's really necessary, but knowing about orthogonal polynomials would be helpful too.
> something I can catch up on in a weekend?
Probably not. If you know any calculus (even a basic high school class should be enough), two weekends would probably be enough; if you don't know calculus, then double it.
My advice would be to use an introductory level quantum physics textbook or an advanced chemistry textbook, since the spherical harmonics are used quite a bit in those fields. You could use a math textbook too, but those will tend to focus on details that are irrelevant to you.
An alternate path would be to learn about Fourier series/transformations, then what's discussed in the article will follow as a natural consequence. This is probably a harder option, but there's lots of really good learning materials online for Fourier transformations (and comparatively little for spherical harmonics), so it may end up being easier for you.