analytic function

Function that is locally given by a convergent power series

EntityQ215084

Subclass of: smooth function

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From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at a point if, in some neighborhood of that point, it is equal to a power series centered there. The analytic function is therefore locally determined by coefficients of the series, or equivalently by derivatives of the function evaluated at the center of the series expansion. In other words, an analytic function is a function that is locally represented by a convergent Taylor series.

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27 statements · 33% with external sources · numbers in brackets are citations

Different from: smooth function

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25 identifiers linking analytic function across the web's reference databases

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33%

externally sourced

Source last edited October 3, 2026. AIDB refreshes this page daily.

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AIDB. (2026). analytic function (Q215084). Retrieved from https://aidb.si/e/analytic-function-Q215084