DiracDelta[x] represents the Dirac delta function .
DiracDelta[, , ... ] represents the multidimensional Dirac delta function .
DiracDelta[x] returns 0 for all 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[, , ... ] returns 0 if any of the are 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.
See The Mathematica Book: Section 3.5.12.
See also: UnitStep, If, PrincipalValue, Limit, KroneckerDelta.