Connections within the group of complex components and with other function groups

Representations through more general functions

All six complex component functions , , , , , and cannot be easily represented by more generalized functions because most of them are analytic functions of their arguments. But sometimes such representations can be found through Meijer G functions, for example:

Representations through other functions

All six complex components , , , , , and satisfy numerous internal relations of the type , where and are different complex components and is a basic arithmetic operation or (composition of) elementary functions. The most important of these relations are represented in the following table:

Other internal relations between complex components of the type , where and are different complex components that also exist. Some of them are shown here:

Here are some more formulas of the last type:

(here is the Heaviside theta function, also called the unit step function).

The first table can be rewritten using the notations :