Editing Harmonic function (section)

==Etymology of the term "harmonic"==
The descriptor "harmonic" in the name "harmonic function" originates from a point on a taut string which is undergoing [[simple harmonic motion|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|''n''-sphere]], one arrives at the [[spherical harmonics]]. These functions satisfy Laplace's equation and, over time, "harmonic" was [[synecdoche|used to refer to all]] functions satisfying Laplace's equation.<ref>{{cite book |last1=Axler |first1=Sheldon |last2=Bourdon |first2=Paul |last3=Ramey |first3=Wade |date=2001 |title=Harmonic Function Theory |url=https://archive.org/details/harmonicfunction00axle_418 |url-access=limited |location=New York |publisher=Springer |page=[https://archive.org/details/harmonicfunction00axle_418/page/n34 25] |isbn=0-387-95218-7}}</ref>