represents the Dirac delta function .
represents the multidimensional Dirac delta function .
- DiracDelta[x] returns 0 for all real numeric x other than 0.
- DiracDelta can be used in integrals, integral transforms, and differential equations.
- Some transformations are done automatically when DiracDelta appears in a product of terms.
- DiracDelta[x1,x2,…] returns 0 if any of the xi are real numeric and not 0.
- DiracDelta has attribute Orderless.
- For exact numeric quantities, DiracDelta 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 (3)
Numerical Evaluation (4)
Specific Values (3)
As a distribution, DiracDelta does not have a specific value at 0:
Function Properties (4)
Integrate expressions containing derivatives of DiracDelta:
Compare with the direct result from DSolve:
Higher derivatives will contain DiracDelta:
Using Piecewise does not recover the original function:
Incorporate the initial values in the right‐hand side through derivatives of DiracDelta:
Properties & Relations (4)
Possible Issues (8)
DiracDelta is not an "infinite" quantity:
DiracDelta can stay unevaluated for numeric arguments:
DiracDelta cannot be uniquely defined with complex arguments:
Neat Examples (1)
Do it using the dual Taylor expansion expressed in derivatives of DiracDelta: