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* The Fourier series of a periodic odd function includes only [[trigonometric function|sine]] terms.
===Algebraic
* Any [[linear combination]] of even functions is even, and the even functions form a [[vector space]] over the [[real number|real]]s. Similarly, any linear combination of odd functions is odd, and the odd functions also form a vector space over the reals. In fact, the vector space of ''all'' real-valued functions is the [[direct sum]] of the spaces of even and odd functions. In other words, every function can be written uniquely as the sum of an even function and an odd function:
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