Table of Contents
Meaning of Analytic Function
Analytic Function – Meaning: An analytic function is a function that is defined by a power series. The power series is centered at a point in the complex plane and converges to the function at that point.
Types of Analytic Functions
There are three main types of analytic functions: power, exponential, and logarithmic.
- A power function is a type of analytic function in which the independent variable raised to a power. For example, y = x^2 is a power function.
- An exponential function is a type of analytic function in which the independent variable multiplied by a constant. For example, y = 2x is an exponential function.
- A logarithmic function is a type of analytic function in which the independent variable raised to the power of a logarithm. For example, y = log(x) is a logarithmic function.
Real Analytic Function
An analytic function a function that can expressed as a power series in a neighborhood of a given point.
Complex Analytic Function
In mathematics, a complex analytic function is a function that is analytic in a complex domain.
A complex analytic function is a function that is analytic in a complex domain. In other words, it is a function that can expressed as a Taylor series in a neighborhood of every point in its domain.
Conditions that Make a Complex Function Analytic
A complex function is analytic at a point if it is continuous and also its derivative is continuous at that point.
Properties of Analytic Function
- An analytic function is continuous on a closed and bounded interval and differentiable at every point in the interval.
- Function is a set of ordered pairs (x, y) such that to each element of x corresponds a unique element of y. An analytic function is a function that can given by a power series in a neighborhood of each point in its domain.
- A function said to have a power series representation about a, if f(x) can written as a series of terms involving the powers of the quantity (x-a).
