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−a 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:

or:

Indeed: