# HeavisidePi

HeavisidePi[x]

represents the box distribution , equal to 1 for and 0 for .

HeavisidePi[x1,x2,]

represents the multidimensional box distribution which is 1 if all .

# Details • HeavisidePi[x] returns 0 or 1 for all numeric x other than -1/2 and 1/2.
• HeavisidePi[x] is equivalent to .
• HeavisidePi can be used in derivatives, integrals, integral transforms and differential equations.
• HeavisidePi has attribute

# Examples

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## Basic Examples(4)

Evaluate numerically:

Plot in one dimension:

Plot in two dimensions:

The derivative generates DiracDelta distributions:

## Scope(30)

### Numerical Evaluation(4)

Evaluate numerically:

HeavisidePi always returns an exact result:

Evaluate efficiently at high precision:

### Specific Values(4)

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:

### Visualization(4)

Plot the HeavisidePi function:

Visualize scaled HeavisidePi functions:

Visualize the composition of HeavisidePi with a periodic function:

Plot HeavisidePi in three dimensions:

### Function Properties(6)

Function domain of HeavisidePi:

It is restricted to real inputs:

Approximate function range of HeavisidePi:

HeavisidePi is an even function:

The area under HeavisidePi is 1:

HeavisidePi has a jump discontinuity at the points :

### Differentiation (4)

Differentiate the univariate HeavisidePi:

Differentiate the multivariate HeavisidePi:

Higher derivatives with respect to z:

Differentiate a composition involving HeavisidePi:

### Integration(4)

Integrate over finite domains:

Integrate over infinite domains:

Numerical integration:

Integrate expressions containing symbolic derivatives of HeavisidePi:

### Integral Transforms(4)

The FourierTransform of a unit box is a Sinc function:

Find the LaplaceTransform of a unit box:

The convolution of HeavisidePi with itself is HeavisideLambda:

## Properties & Relations(2)

The derivative of HeavisidePi is a distribution:

The derivative of UnitBox is a piecewise function:

HeavisidePi can be expressed in terms of HeavisideTheta: