# Fourier series

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## 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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## 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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The Fourier expansion of the Poincare series for [[GAMMA].sup.+.sub.0](p).
In addition, they appear in numerical analysis, for instance in the context of the modulated Fourier expansion [9, 17], adiabatic integrators [17, 25] as well as Lawson-type Runge-Kutta methods [24].
To estimate the time derivative term in the unsteady flow governing equations, the time-marching method employs a finite difference method, while time-spectral methods used in this study apply a discrete Fourier expansion and Chebyshev polynomials.
Caption: Figure 1: The graph of [absolute value of ([R.sub.N](f,x))] on [-0.7,0.7] for N = 64 while approximating (53) by the modified Fourier expansion (2).
First, we define a continuous curve c(t) in order to explain a Fourier Expansion (see Figure 8).
According to the uniqueness theorem of Fourier expansion, equating the coefficient [M.sub.nm] in (26),
Since the stiffness is periodically time-varying with the mesh frequency, its analytical formulation can be obtained by means of a Fourier expansion [15]:
where [delta](x) is a continuous periodic function of period 1, mean zero, small amplitude and Fourier expansion
If the boundary is closed, it can be performed by the Fourier expansion in the two coordinate directions to calculate Fourier coefficients.
The concept of Fourier expansion is involved in the resistive boundary condition.
If the covariance function of X has the following Fourier expansion

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