funkcja analityczna

Suppose further that a/a and a/a are analytic functions.

No such results, however, are valid for more general classes of differentiable or real analytic functions.

Hence the theory of the real ordered field with restricted analytic functions is model complete.

This is a continuous mapping, but not an analytic function.

In both cases f is an analytic function on the corresponding open half plane.

These are all analytic functions of the left hemisphere.

However, especially for complex analytic functions, new and interesting phenomena show up when working in 2 or more dimensions.

One can easily prove that any analytic function of a real argument is smooth.

Also note that it would be equivalent to begin with an analytic function defined on some small open set.

One of its main ingredients is the following rather well known result about analytic functions.