Typically, spherical harmonics are introduced as a complex function over spherical coordinates, which makes them much easier to derive, but imo hides their beauty.

The real-valued, cartesian form of regular spherical harmonics is also called "solid harmonics" or "harmonic polynomials", in case you want to dig deeper.

This math is also used in Ambisonic surround sound though newer techniques use planewave expansion.

For games, the full-sphere encoding of Ambisonic B-format can be decoded for arbitrary speaker locations and the soundfield rotated around any axis. I'm not sure if its ever been used for a game though.

Like, if you know the third order harmonics that's only 16 values you have to pass around