analytic function
The term "analytic function" is pivotal in mathematical analysis, particularly in complex analysis, where it describes functions with specific differentiability and series expansion properties.
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Definition
C1Complex Analysis
(technical, academic)A function that is differentiable at every point in a region of the complex plane and can be represented by a convergent power series around each point.
Example
- In complex analysis, an analytic function is also known as a holomorphic function.
- The function f(z) = e^z is an example of an analytic function in the complex plane.
C1Mathematical Analysis
(technical, academic)A function that can be expressed as a convergent power series in a neighborhood around any point in its domain.
Example
- Any polynomial is an analytic function because it can be written as a finite power series.
- The exponential function is analytic because it can be expanded into an infinite power series.
Similar
Terms that have similar or relatively close meanings to "analytic function":
analytic continuationalgebraic analysistranscendental functionmeasurable functioncontinuous function