When Is a Functions Analytic?

A function f(z) is analytic if it has a complex derivative f (z). In general, the rules for computing derivatives will be familiar to you from single variable calculus. However, a much richer set of conclusions can be drawn about a complex analytic function than is generally true about real differentiable functions.

How do you know if a function is analytic?

A function f(z) is said to be analytic in a region R of the complex plane if f(z) has a derivative at each point of R and if f(z) is single valued. A function f(z) is said to be analytic at a point z if z is an interior point of some region where f(z) is analytic.

What makes a function analytic?

In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex 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.