A catalogue of analytic functions.

We define functions according to the following requirements:

• The function should be analytic on its domain.
• The restriction to the reals of the defined function should be the corresponding real function; e.g., we define an exponential $e^z, z \in \mathbb{C}$ such that, if $z=x \in \mathbb{R}$ , then $e^z=e^x$ is the well-known exponential of a real number.