Even and odd functions: Difference between revisions

Revision as of 23:49, 2 May 2023

Revision as of 09:36, 22 January 2024

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[[File:Développement limité du cosinus.svg|thumb|The [[cosine function]] and all of its [[Taylor polynomials]] are even functions. This image shows <math>\cos(x)</math> and its Taylor approximation of degree 4.]]

In [[mathematics]], '''even functions''' and '''odd functions''' are [[function (mathematics)|function]]s which satisfy particular [[symmetrySymmetry in mathematics]] relations, with respect to taking [[additive inverse]]s. They are important in many areas of [[mathematical analysis]], especially the theory of [[power series]] and [[Fourier series]]. They are named for the [[parity (mathematics)|parity]] of the powers of the [[Power Function|power functions]] which satisfy each condition: the function <math>f(x) = x^n</math> is an even function if ''n'' is an even [[integer]], and it is an odd function if ''n'' is an odd integer.

==Definition and examples==