HeavisidePi—Wolfram Language Documentation (original) (raw)
BUILT-IN SYMBOL
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:
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:
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)
Function Properties (12)
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)
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)
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_2025_heavisidepi, author="Wolfram Research", title="{HeavisidePi}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/HeavisidePi.html}", note=[Accessed: 10-June-2025 ]}
BibLaTeX
@online{reference.wolfram_2025_heavisidepi, organization={Wolfram Research}, title={HeavisidePi}, year={2008}, url={https://reference.wolfram.com/language/ref/HeavisidePi.html}, note=[Accessed: 10-June-2025 ]}