# 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

## 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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c] in the interval [0,1 + d] (which also provides an approximation for f in the interval [0,1]) is highly accurate, and it provides, in particular, the needed Fourier expansion of the function f in the interval [0,1].
where [delta](x) is a continuous periodic function of period 1, mean zero, small amplitude and Fourier expansion
The literature review shows that one of the most common mathematical tools to deal with periodical functions is the Fourier expansion, which is an approximation used to rebuild curves based on sinusoidal signals.
If the covariance function of X has the following Fourier expansion
However, one of the major numerical issues in dealing with field-material interactions in a spectral basis is the observation that a simple product equation in real space is not always accurately reproduced by a convolution in Fourier space if one or both representations of the product variables have a finite (or truncated) Fourier expansion (as is the case in numerical implementations).
In this section, we present the Fourier EXpansion simulation ENvironment (FEXEN), which is the simulation tool that we present in this paper.
One derives the latter sampling formula from the Fourier expansion of the function g = [H.
sub/n] and do not lead directly to the Fourier expansion (11) below for log[GAMMA](x).
As a particular consequence of our analysis, we obtain a Fourier expansion theorem in each left-definite space [H.
They use a Fourier expansion to estimate the time trend in house prices.
Performing Fourier expansion, we have refined the fundamental frequency of pulsation for BQ Serpens to be 0.

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