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Built-in Mathematica Symbol

DiscreteDelta

DiscreteDelta[n₁, n₂, ...]
gives the discrete delta function

(n₁, n₂, ...), equal to 1 if all the n_i are zero, and 0 otherwise.

Use in sums:

Use in sums:

One-argument form:

Multi-argument form:

Arguments can be approximate numbers:

Use in sums to pick out terms:

Pick out elements:

Patch pointwise values of piecewise-defined functions:

Reduce an equation containing DiscreteDelta:

The support of DiscreteDelta has measure zero:

DiscreteDelta can stay unevaluated with numeric arguments:

A larger setting for $MaxExtraPrecision can be needed:

Equality testing of the arguments takes numerical precision into account: