What is a Linear Combination of Spherical Harmonics?

[Fyrefly]

I didn't get any bites in the Calculus section a few days ago so I'm hoping since this is likely a pretty basic part of spherical harmonics that someone here can aid me. Also hoping reposting in a new section after a few days is allowed. Thank you in advance for your assistance!

Homework Statement

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

Homework Equations

See below

The Attempt at a Solution

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[1,0] + C*Y[1,1]

Where Y values are the spherical harmonics in the form Y[order, rank].

So to fit my model I would need to determine coefficients A, B, and C. Am I doing the linear combination right?

 

[Nino MMP]

Is this the way one would normally solve a problem like this? If not, what is the correct way? Any help would be appreciated!