 
 
 
9.2.1  Defining periodic expressions
The periodic command creates
periodic expressions.
- 
periodic takes two or four arguments:
- 
expr, an expression f(x) where x∈[a,b⟩ for a<b.
- x, a real variable.
- a, a real number specifying the lower bound for x.
- b, a real number specifying the upper bound for x.
 The last three arguments can be passed as a single argument x=a..b.
- periodic(expr,x,a,b) or
periodic(expr,x=a..b)
returns a periodic expression
| g(x)=f | ⎛ ⎜
 ⎜
 ⎝
 | x−(b−a) | ⎢ ⎢
 ⎢
 ⎣
 |  | ⎥ ⎥
 ⎥
 ⎦
 | ⎞ ⎟
 ⎟
 ⎠
 | ,   x∈ℝ, |  
 with period T=b−a, satisfying the property g(x+T)=g(x) for all x∈ℝ.
Example
To define the periodic function f(x)=1−x2 for −1≤ x<1 with period T=2, input:
| f:=periodic(1-x^2,x,-1,1) | 
or:
| f:=periodic(1-x^2,x=-1..1) | 
|  | | | − | ⎛ ⎜
 ⎜
 ⎝
 | −2 | ⎢ ⎢
 ⎢
 ⎣
 |  | ⎥ ⎥
 ⎥
 ⎦
 | +x | ⎞ ⎟
 ⎟
 ⎠
 |  | +1 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
Indeed:
 
 
