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that is,

everywhere on . This is usually written as

or

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

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