Evaluate numerically:

Complex number inputs:

DiscreteDelta always returns an exact result irrespective of the precision of the input:

Evaluate efficiently at high precision:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix DiscreteDelta function using MatrixFunction:

Value at zero:

Multi‐argument form gives 1 when all inputs are zero:

Value at infinity:

Evaluate symbolically:

Plot the single-argument DiscreteDelta using integer-width bins:

Visualize DiscreteDelta over the reals. Except for a jump at , it is indistinguishable from a zero function:

Plot DiscreteDelta in three dimensions:

DiscreteDelta is defined for all real and complex inputs:

Function range of DiscreteDelta:

The function range for complex values is the same:

DiscreteDelta is not an analytic function:

Has both singularities and discontinuities:

DiscreteDelta is neither nondecreasing nor nonincreasing:

DiscreteDelta is not injective:

DiscreteDelta is not surjective:

DiscreteDelta is non-negative:

DiscreteDelta is neither convex nor concave:

TraditionalForm typesetting:

First derivative with respect to x:

Series expansion at a generic point:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

More integrals: