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Enervation (talk | contribs) Add link in {{about}} to analytic function (SQL) |
Disambiguated analytic function → Window function. |
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{{short description|Function locally given by a convergent power series}}
{{Distinguish|analytic expression|analytic signal}}
{{about|both real and complex analytic functions|analytic functions in complex analysis specifically|holomorphic function|analytic functions in SQL|
{{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'''. Functions of each type are [[smooth function|infinitely differentiable]], but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its [[Taylor series]] about ''x''<sub>0</sub> converges to the function in some [[neighborhood (topology)|neighborhood]] for every ''x''<sub>0</sub> in its [[Domain of a function|___domain]].
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