What is an "analytic function"?

Question

Mathematics

What are analytic functions?
Can you give simple examples of such functions?

Answer 1

Wikipedia describes everything in detail:
Analytic function
In the complex plane, a function that is differentiable at each point of the region (examples: polynomials, exp, sin, cos are analytical on the entire plane, and sqrt and ln are outside the ray x <= 0).
On the real line, an infinitely differentiable function that coincides with its Taylor series at every point. Almost any infinitely differentiable functions are suitable, but, for example, exp(-1/x^2) will not be analytic at zero - all its derivatives there, and hence the Taylor series, are equal to zero.