Fourier series

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Related to Fourier series: Fourier transform
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the sum of a series of trigonometric expressions

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The idea of using truncated Fourier series expansions is introduced in Section 2.
We investigated pointwise approximation of modified conjugate functions by matrix operators of their Fourier series. In particular, we estimated the deviation [mathematical expression not reproducible] by the function of modulus of continuity type in the case when conjugate function [f.sub.r] depends on r.
According to [20], the displacement [u.sub.k.sup.[infinity]] and stress fields [[sigma].sub.jk.sup.[infinity]] of the infinite dislocation set can be written in the O[x.sub.1][x.sub.2][x.sub.3] frame in the form of double Fourier series. The [[sigma].sub.jk.sup.[infinity]] stress field can be expressed as (integers m, n [not equal to] 0)
Let us search for the solution of the system of Fredholm integral equations (11) in the form of Fourier series as follows:
By using SAFEM, the general form of the shape functions defining the variation of displacements can be written as a Fourier series in which z ranges between zero and a, as shown in Figure 4 [18-27, 39].
Smith also discussed the convolution for [S'.sub.1] and [P.sup.*.sub.p] and Fourier series of [S'.sub.1] in [17].
In this paper, we adopt a finite Fourier series which was proposed by Swevers et al.
Adcock, "Multivariate modified Fourier series and application to boundary value problems," Numerische Mathematik, vol.
Schaeffer, "A class of nonharmonic Fourier series," Transactions of the American Mathematical Society, vol.
The error of the Fourier series approximation model satisfies the filling requirement when it is less than 1%.
Dendrinos [1] considered traffic as a combination of 17 periodic components and residual parts and as fitting the trend with Fourier series. Fei et al.
In [20, 21], for Lebesgue spaces [L.sub.p], some estimates were obtained for the norms and moduli of smoothness of transformed Fourier series which coincides up to notation with the Fourier series of the ([psi], [beta])-derivatives.