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Em3rgent0rdr (talk | contribs) →Even–odd decomposition: I also hear "component" used instead of "part". |
Em3rgent0rdr (talk | contribs) →Even–odd decomposition: ending section with sentence linking to sine and cosine transforms. |
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For example, the [[hyperbolic cosine]] and the [[hyperbolic sine]] may be regarded as the even and odd parts of the exponential function, as the first one is an even function, the second one is odd, and
:<math>e^x=\underbrace{\cosh (x)}_{f_\text{even}(x)} + \underbrace{\sinh (x)}_{f_\text{odd}(x)}</math>.
[[Joseph Fourier|Fourier]]'s [[sine and cosine transforms]] also perform even–odd decomposition by representing a function's odd part with [[sine waves]] (an odd function) and the function's even part with cosine waves (an even function).
==Further algebraic properties==
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