Domain and analyticity
In the majority of cases, is an analytical function of , which is defined in the whole complex plane (if special restrictions are not shown).
Symmetries and periodicities
This formula is the condition for a function to be even. For example, the function is an even function.
This formula is the condition for a function to be odd. For example, the function is an odd function.
This formula reflects periodicity of function (if is periodic with period ). The analytic function is called periodic if there exists a complex constant such that . The number (with minimal value ) is called the period of the function . For example, the functions and have periods and accordingly.