Harmonic function
Etymology of the term "harmonic"

The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion. The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as harmonics. Fourier analysis involves expanding functions on the unit circle in terms of a series of these harmonics. Considering higher dimensional analogues of the harmonics on the unit n -sphere, one arrives at the spherical harmonics. These functions satisfy Laplace's equation and over time "harmonic" was used to refer to all functions satisfying Laplace's equation.
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