# cosine series

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Related to cosine series: Fourier sine series

## cosine series

[′kō‚sīn ‚sir·ēz]
(mathematics)
A Fourier series that contains only terms that are even in the independent variable, that is, the constant term and terms involving the cosine function.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In order to derive the constraint equations for the unknown coefficients, all the sine terms and the auxiliary series functions will be expanded into Fourier cosine series. The related formulas are provided in Appendix A.
By substituting (4) into the governing differential equation (1), as mentioned earlier, all the sine terms and the auxiliary series functions are expanded into Fourier cosine series.
So it is clear that as our estimate for [pi] gets better, we must include more terms in our sine and cosine series in subsequent iterations.
We observe that the above theorems provide just only sufficient conditions for the integrability of cosine series. Rees and Stanojevic [6] show [[infinity].summation over (k=1)] [a.sub.k]/k < [infinity] is a necessary and sufficient condition for [L.sup.1] (0,[pi]] integrability but for a different type of cosine sum
Bishop, "The Classical Truncated Cosine Series Functions with Applications to SAW Filters," IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol.
To unify the descriptions and facilitate the analytical calculations of the involved integrals, all these distribution functions can be expanded into 1-D or 2-D Fourier cosine series.
where the nodal function [C.sub.k] is a bivariate cosine series that interpolates the data value [f.sub.k] at node k and fits the data values on a set of nearby nodes in a weighted least-squares sense.
The gear motion error is a real signal, described by an infinite cosine series with fundamental period f r.

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