FunctionPeriod[f,x]
gives a period p of the function f over the reals such that 
.
FunctionPeriod[{f1,f2,…},{x1,x2,…},…]
gives periods {p1,p2,…} for {x1,x2,…} such that 
.
FunctionPeriod
FunctionPeriod[f,x]
gives a period p of the function f over the reals such that 
.
FunctionPeriod[f,x,dom]
gives a period with x restricted to the domain dom.
FunctionPeriod[{f1,f2,…},{x1,x2,…},…]
gives periods {p1,p2,…} for {x1,x2,…} such that 
.
Examples
open all close allBasic Examples (3)
Scope (9)
Basic Uses (4)
Periodic Functions over the Integers (5)
Basic periodic sequences include Mod:
Mod of a polynomial:
And in general powers of roots of unity, i.e. roots of the polynomial 
:
A common way to express these are 
:
Trigonometric functions with a rational multiple of their real period:
A function 
where 
is periodic over the reals with period 
and 
rational:
It works similarly for a function periodic over the complexes:
Any finite sum of periodic sequences is periodic:
Text
Wolfram Research (2014), FunctionPeriod, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionPeriod.html.
CMS
Wolfram Language. 2014. "FunctionPeriod." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FunctionPeriod.html.
APA
Wolfram Language. (2014). FunctionPeriod. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionPeriod.html