Evaluate numerically:

HeavisidePi always returns an exact result:

Evaluate efficiently at high precision:

HeavisidePi threads over lists:

Compute average-case statistical intervals using Around :

Compute the elementwise values of an array:

Or compute the matrix HeavisidePi function using MatrixFunction :

Value at zero:

As a distribution, HeavisidePi does not have specific values at :

Evaluate symbolically:

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

Plot the HeavisidePi function:

Visualize scaled HeavisidePi functions:

Visualize the composition of HeavisidePi with a periodic function:

Plot HeavisidePi in three dimensions:

Function domain of HeavisidePi :

It is restricted to real inputs:

Function range of HeavisidePi :

HeavisidePi is an even function:

The area under HeavisidePi is 1:

HeavisidePi has a jump discontinuity at the points :

HeavisidePi is not an analytic function:

It has both singularities and discontinuities:

HeavisidePi is neither nonincreasing nor nondecreasing:

HeavisidePi is not injective:

HeavisidePi is not surjective:

HeavisidePi is non-negative on its domain:

HeavisidePi is neither convex nor concave:

TraditionalForm formatting:

Differentiate the univariate HeavisidePi :

Differentiate the multivariate HeavisidePi :

Higher derivatives with respect to z:

Differentiate a composition involving HeavisidePi :

Integrate over finite domains:

Integrate over infinite domains:

Numerical integration:

Integrate expressions containing symbolic derivatives of HeavisidePi :

The FourierTransform of a unit box is a Sinc function:

FourierSeries :

Find the LaplaceTransform of a unit box:

The convolution of HeavisidePi with itself is HeavisideLambda :