# Fourier series

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Related to Fourier series: Fourier transform

## Fourier series

n.
An infinite series whose terms are constants multiplied by sine and cosine functions and that can, if uniformly convergent, approximate a wide variety of functions.

[After Baron Jean Baptiste Joseph Fourier.]

## Fourier series

n
(Mathematics) an infinite trigonometric series of the form a0 + a1cos x + b1sin x + a2cos 2x + b2sin 2x + …, where a0, a1, b1, a2, b2 … are the Fourier coefficients. It is used, esp in mathematics and physics, to represent or approximate any periodic function by assigning suitable values to the coefficients

## Fou′rier se`ries

n.
an infinite series that approximates a given function on a specified domain by using linear combinations of sines and cosines.
[1875–80; see Fourier analysis]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Fourier series - the sum of a series of trigonometric expressions; used in the analysis of periodic functionsseries - (mathematics) the sum of a finite or infinite sequence of expressions
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Given a function of class Lp let us consider its conjugate trigonometric Fourier series
In synchronous rotating space coordinates, flux linkage are reconstructed through Fourier series expansion and bivariate polynomial.
This undergraduate textbook introduces the nature and significance of differential equations as a tool for studying change in the physical world, progressing from first- and second-order linear equations to Fourier series, boundary value problems, Laplace transforms, nonlinear equations, and the calculus of variations.
Here, we think of the DFT or DCT as approximations for the Fourier series or cosine series of a function, respectively, in order to talk about its "smoothness") However, the implicit periodicity of the DFT means that discontinuities usually occur at the boundaries: any random segment of a signal is unlikely to have the same value at both the left and right boundaries.
be the Fourier series of a function f [member of] [L.
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Differentiation of Fourier series is, of course, straightforward and, in view of the Fast Fourier Transform, can be produced in 0(N log N) operations, where N is the number of points in the mesh.
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The method is named for the French mathematician and physicist Jean Baptiste Joseph, Baron de Fourier, and developed from his original work, known as the Fourier series.
Its oscillations are not smooth, so that they are not readily describable by Fourier series.
The matching process for obtaining the Fourier series solution to the Poisson's problems defined in the T-shaped geometry produced an infinite system of algebraic equations for the unknown expansion coefficients.
More difficult topics include sequences and series of functions, Fourier series, functions of several variables, an in-depth exploration of derivatives, implicit functions and optimization, parametric integration, and integration in Rn.

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