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CecilBlade (talk | contribs) →Basic properties: -product of even and odd function |
the terminology "identically" is more standard than "everywhere" (I also put "i.e. f(x) = 0 for all x") |
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===Basic properties===
* The only function which is ''both'' even and odd is the [[constant function]] which is
* In general, the [[addition|sum]] of an even and odd function is neither even nor odd; e.g. ''x'' + ''x''<sup>2</sup>.
* The sum of 2 even functions is even, and any constant multiple of an even function is even.
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* The [[Taylor series]] of an even function includes only even powers.
* The
* The [[Fourier series]] of a [[periodic]] even function includes only [[trigonometric function|cosine]] terms.
* The
===Algebraic Structure===
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