Evaluate numerically:

Evaluate with custom heights:

SquareWave[x] always returns an exact result:

SquareWave[{min,max},x] generally tracks the precision of {min,max}:

Evaluate efficiently at high precision:

SquareWave threads over lists in the last argument:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix SquareWave function using MatrixFunction:

Value at zero:

Values at fixed points:

Evaluate symbolically:

Find a value of x for which the SquareWave[{2,-3},x]=2:

Plot the SquareWave function:

Visualize scaled SquareWave functions:

Visualize SquareWave functions with different maximum and minimum values:

Plot SquareWave in three dimensions:

Function domain of SquareWave:

It is restricted to real inputs:

Function range of SquareWave[x]:

SquareWave is periodic with period 1:

SquareWave is an odd function:

The area under one period is zero:

SquareWave is not an analytic function:

It has both singularities and discontinuities on the integers:

SquareWave[x] is neither nondecreasing nor nonincreasing:

SquareWave is not injective:

SquareWave[x] is not surjective:

SquareWave[x] is neither non-negative nor non-positive:

SquareWave is neither convex nor concave:

First derivative with respect to :

Derivative of the two-argument form with respect to :

If a==b, SquareWave[{a,b},x] is constant and its derivatives are zero everywhere:

Compute the indefinite integral using Integrate:

Verify the anti-derivative away from the singular points:

More integrals:

FourierSeries:

Since SquareWave is odd, FourierTrigSeries gives a simpler result:

The two results are equivalent:

FourierCosSeries of a scaled SquareWave:

Taylor series at a smooth point:

Series expansion at a singular point:

Taylor expansion at a generic point: