Properties of periodic function

Properties of periodic function

The properties of periodic functions are divided into the following types
(1) if t (≠ 0) is the period of F (x), then - t is also the period of F (x)
(2) if t (≠ 0) is the period of F (x), then NT (n is any nonzero integer) is also the period of F (x)
(3) if T1 and T2 are f (x) periods, then T1 ± T2 is also f (x) period
(4) if f (x) has the smallest positive period T *, then any positive period T of F (x) must be a positive integer multiple of T *
(5) if T1 and T2 are two cycles of F (x), and T1 / T2 is not irrational, then f (x) has a minimum positive period
(6) if T1 and T2 are two cycles of F (x), and T1 / T2 are irrational numbers, then f (x) has no minimum positive period
The domain m of periodic function f (x) must be an unbounded set of at least one side