# 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 .

# Examples

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## Basic Examples(4)

Evaluate numerically:

Plot in one dimension:

Plot in two dimensions:

The derivative generates DiracDelta distributions:

## Scope(38)

### Numerical Evaluation(6)

Evaluate numerically:

HeavisidePi always returns an exact result:

Evaluate efficiently at high precision:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix HeavisidePi function using MatrixFunction:

### 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(12)

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:

### 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:

## Applications(2)

Integrate a function involving HeavisidePi symbolically and numerically:

Solve an initial value problem for the heat equation:

Specify an initial value:

Solve the initial value problem using :

Compare with the solution given by DSolveValue:

## 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:

Wolfram Research (2008), HeavisidePi, Wolfram Language function, https://reference.wolfram.com/language/ref/HeavisidePi.html.

#### Text

Wolfram Research (2008), HeavisidePi, Wolfram Language function, https://reference.wolfram.com/language/ref/HeavisidePi.html.

#### CMS

Wolfram Language. 2008. "HeavisidePi." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HeavisidePi.html.

#### APA

Wolfram Language. (2008). HeavisidePi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HeavisidePi.html

#### BibTeX

@misc{reference.wolfram_2024_heavisidepi, author="Wolfram Research", title="{HeavisidePi}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/HeavisidePi.html}", note=[Accessed: 03-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_heavisidepi, organization={Wolfram Research}, title={HeavisidePi}, year={2008}, url={https://reference.wolfram.com/language/ref/HeavisidePi.html}, note=[Accessed: 03-August-2024 ]}