Evaluate numerically:

UnitBox always returns an exact result:

Evaluate efficiently at high precision:

UnitBox threads over lists:

Value at zero:

Values at the points of discontinuity:

Evaluate symbolically:

Find a value of x for which UnitBox[x]=1:

Plot the UnitBox function:

Visualize scaled UnitBox functions:

Visualize the composition of UnitBox with a periodic function:

Plot UnitBox in three dimensions:

Function domain of UnitBox:

It is restricted to real inputs:

Function range of UnitBox:

UnitBox is an even function:

The area under UnitBox is 1:

UnitBox has a jump discontinuity at the points :

UnitBox is not an analytic function:

It has both singularities and discontinuities:

UnitBox is neither nonincreasing nor nondecreasing:

UnitBox is not injective:

UnitBox is not surjective:

UnitBox is non-negative:

UnitBox is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to x:

All higher-order derivatives are the same:

First derivative with respect to z:

Compute the indefinite integral using Integrate:

Verify the anti-derivative away from the singular points:

Definite integral:

Integral over an infinite domain:

The FourierTransform of a unit box is a Sinc function:

FourierSeries:

Find the LaplaceTransform of a unit box:

The convolution of UnitBox with itself is UnitTriangle: