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...y of the conduction of heat in terms of sums of trigonometric functions, [[Fourier series]], which finds application in the propagation of sound; the propagation of

...important papers were a series of publications on definite integrals and [[Fourier series]]. This latter work paved the way for [[Peter Dirichlet]] and [[Bernhard Ri

...omponent. There is still an associated eigenfunction expansion (similar to Fourier series versus Fourier transform). This is important in [[quantum mechanics]], sinc ...of a S–L problem form an orthogonal basis, and we know from the theory of Fourier series that this set of sinusoidal functions is an orthogonal basis. Since orthogo

* [[Joseph Fourier|Fourier, Joseph]] (1768-1830) - invented of Fourier series (long before electronic computers), making possible imaging algorithms for

...math>, the series with terms <math> c_n e^{inx} </math> is also treated as Fourier series. ...matics)|distributions (generalized functions)]] also may be developed into Fourier series, in which case convergence is much weaker.

...ifferences in tone between [[musical instrument]]s can be analyzed using [[Fourier series]] to identify the frequencies comprising the tone.<ref name=Gunther/> ...sical note by its constituent frequency components, in the same way that a Fourier series expresses a periodic waveform in terms of its harmonic components.

...reatment of trigonometric functions and their applications (''e.g.,'' in [[Fourier series]]), since the theory of [[infinite series]] can be developed from the found ...ential equations. For example the [[square wave]], can be written as the [[Fourier series]]

...basis sets are a generalization of the sine and cosine functions used in [[Fourier series]] to a wider set of functions, a subject sometimes called ''generalized Fou

...'' in a Taylor expansion of a function ''f(x)'', or sines and cosines in a Fourier series.

...ers could be (for example) coefficients in a functional expansion like a [[Fourier series]]. In a physical problem, they could be [[spacetime]] coordinates or [[norm

...mathematics in Vienna. Her Ph.D. was awarded in 1917 for a thesis on the [[Fourier series]] in two variables. She spent the following two years as Leon Lichtenstein'