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

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:

HeavisidePi threads over lists:

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 :

TraditionalForm formatting:

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:

FourierSeries:

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:

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.

BibTeX

@misc{reference.wolfram_2021_heavisidepi, author="Wolfram Research", title="{HeavisidePi}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/HeavisidePi.html}", note=[Accessed: 18-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_heavisidepi, organization={Wolfram Research}, title={HeavisidePi}, year={2008}, url={https://reference.wolfram.com/language/ref/HeavisidePi.html}, note=[Accessed: 18-September-2021 ]}

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