# What is a Linear Combination of Spherical Harmonics?

• Fyrefly

#### Fyrefly

Okay, so I'm working on using spherical harmonics to fit a model to some data. The thing is, everything can apparently be described as a "linear combination of spherical harmonics" but nobody is explaining in plain English what that means, at least to me! :D

I see lots of double sum equations and everybody seems to solve spherical harmonics in a different way. So what I'd like to know, is this right? Based on the table of spherical harmonics I think a linear combination to get a 1st order spherical harmonic of them would look something like:

E(θ, $\varphi$) = A*Y[0,0] + B*Y[-1,1] + C*Y[0,1] + D*Y[1,1].

So to fit my model I would need to determine coefficients A, B, C, and D. Is this right? Also, is there a particular way to do it for real-valued spherical harmonics? I don't have imaginary numbers in my data and this isn't a plotting exercise so I'm not sure what to do with them.

Did I put this in the wrong section? I'd love some help when someone can manage the time. Thanks.