We first need to define a periodic function. A function is called periodic with period if , for all , even if is not defined everywhere. A simple example is the function which is periodic with period . Of course it is also periodic with periodic . In general a function with period is periodic with period . This can easily be seen using the definition of periodicity, which subtracts from the argument
(4.6) |
The smallest positive value of for which is periodic is called the (primitive) period of .
Question: What is the primitive period of ?
Answer: .