represents the Heaviside theta function , equal to 0 for and 1 for .
represents the multidimensional Heaviside theta function, which is 1 only if all of the xi are positive.
- HeavisideTheta[x] returns 0 or 1 for all real numeric x other than 0.
- HeavisideTheta can be used in integrals, integral transforms, and differential equations.
- HeavisideTheta has attribute Orderless.
- For exact numeric quantities, HeavisideTheta internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
Examplesopen allclose all
Basic Examples (4)
Differentiate to obtain DiracDelta:
Numerical Evaluation (4)
Specific Values (4)
Function Properties (4)
Compare with the direct result from DSolve:
Using Piecewise does not recover the original function:
Properties & Relations (6)
Possible Issues (10)
HeavisideTheta stays unevaluated for vanishing argument:
HeavisideTheta can stay unevaluated for numeric arguments:
Machine‐precision numericalization of HeavisideTheta can give wrong results:
HeavisideTheta cannot be uniquely defined with complex arguments (no Sato hyperfunction interpretation):