I'm after a reading source for a set of 'interesting' functions on the complex plane along $ f:\mathbb{C}^m \rightarrow \mathbb{C}$, complete with definitions that can be used to compute them numerically.

I'm looking for functions bearing graphs with interesting (read: varied) behaviour, or that can be composed in order to generate more diverse ones.

An example building block is the exp function which we can define as

$e^{a \ + \ ib} = e^{a} \ (\cos a + i\sin b)$

which can be immediately implemented numerically.

Functions

• like exp, that can be defined in terms of real ones;
• that have some known algorithm for computing the complex components;
• that are defined in terms of others in the list,

are good.

Does anyone know of a 'list' of such common/interesting computable functions, from books or web (preferably)? Making it up on the spot is good too.

Apologies for the lack of formality :) Thanks!

I'm after a set of 'interesting' functions on the complex plane along with definitions that can be used to compute them numerically.

I'm looking for functions bearing graphs with interesting (read: varied) behaviour, or that can be composed in order to generate more diverse ones.

An example building block is the exp function which we can define as

$e^{a \ + \ ib} = e^{a} \ (\cos a + i\sin b)$

which can be immediately implemented numerically.

Functions

• like exp, that can be defined in terms of real ones;
• that have some known algorithm for computing the complex components;
• that are defined in terms of others in the list,

are good.

Does anyone know of a 'list' of such common/interesting computable functions, from books or web (preferably)? Making it up on the spot is good too.

Apologies for the lack of formality :) Thanks!