Difference between revisions of "Analytic function"
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| − | In [[mathematics]], an '''analytic function''' is a [[Function (mathematics)|function]] that is locally given by a convergent power series. | + | In [[mathematics]], an '''analytic function''' is a [[Function (mathematics)|function]] that is locally given by a [[Convergent series|convergent]] [[power series]]. |
== Description == | == Description == | ||
Latest revision as of 08:32, 9 September 2016
In mathematics, an analytic function is a function that is locally given by a convergent power series.
Description
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 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 x0 converges to the function in some neighborhood for every x0 in its domain.
See also
- Cauchy–Riemann equations
- Holomorphic function
- Infinite compositions of analytic functions
- Paley–Wiener theorem
- Quasi-analytic function
External links
- Analytic function @ Wikipedia
