Fourier series

(redirected from Cosine series)
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Related to Cosine series: Fourier sine series
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the sum of a series of trigonometric expressions

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In this paper, an improved Fourier series method is employed to analyze the free vibration of Mindlin rectangular plates with general elastic boundary supports, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series.
We expand [F.sup.0.sub.p] or [F.sup.e.sub.p] into the sine series and the cosine series, respectively.
It will be instructive first to include terms in our sine and cosine series only up to [x.sup.5].
Concerning the integrability of trigonometric cosine series belonging to the class S, Teljakovskii [7] established the following theorem:
be a cosine series satisfying [a.sub.n] [right arrow] 0 as n [right arrow] [infinity].
From Equation 5, only [b.sub.1] and [b.sub.2] can be determined, and a three-term cosine series results.
More explicitly, the negatively indexed coefficients can be shown to be dependent on those for the cosine series under the condition that the (cosine) series converges fast enough so that it can be differentiated term by term.
It is based on a modified Shepard method similar to that of Algorithm 660 but uses 10-parameter cosine series nodal functions in place of quadratic polynomials.
Even and odd cosine series functions in the time domain that are used as eigen functions for SAW filter realization have been described.[3] As the number of terms (N) in the functions increase, the side lobe levels decrease and the main lobe width increases.