Analytic function: Difference between revisions

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{{about|both real and complex analytic functions|analytic functions in complex analysis specifically|holomorphic function}}

{{Complex analysis sidebar}}

In [[mathematics]], an '''analytic function''' is a [[function (mathematics)|function]] that is locally given by a [[convergent series|convergent]] [[power series]]. There exist both '''real analytic functions''' and '''complex analytic functions''', categories that are similar in some ways, but different in others. Functions of each type are [[smooth function|infinitely differentiable]], but complex analytic functions exhibit properties that do not hold generally for real analytic functions. A function is analytic if and only if its [[Taylor series]] about ''x''₀ converges to the function in some [[neighborhood (topology)|neighborhood]] for every ''x''₀ in its [[Domain of a function|___domain]].

== Definitions ==