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In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function f (x ) = xn is an even function if n is an even integer and it is an odd function if n is an odd integer.