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. | 
