§Let S ÌC
be an open set, and let f(s) be a complex valued function defined on S,f(s) : S ®C. Then f(s) is analytic at a point z0in S if it differentiable at z0andalso at each point in some neighborhood of z0.
•It is a fact
that if f(s) is analytic at z0then f has continuous derivatives
orders at z0. Hence, it has a power series representation at z0.
•A function f(s) is said to be analytic in S if it has a derivative or
is analytic at each point of S.
Theorem: If f(s) is defined and
continuous on a closed-bounded set S and analytic on the interior of S, then