Evaluate numerically:

Complex number inputs:

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

Evaluate efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix KroneckerDelta function using MatrixFunction:

Compute average-case statistical intervals using Around:

Value at zero:

The multi-argument form gives 1 when all inputs are equal:

Evaluate symbolically:

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

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

Plot KroneckerDelta in three dimensions:

KroneckerDelta is defined for all real and complex inputs:

Function range of KroneckerDelta:

The function range for complex values is the same:

KroneckerDelta accepts list inputs:

The traditional notation is used in both StandardForm and TraditionalForm:

KroneckerDelta is not an analytic function:

It has both singularities and discontinuities:

KroneckerDelta is neither nondecreasing nor nonincreasing:

KroneckerDelta is not injective:

KroneckerDelta is not surjective:

KroneckerDelta is non-negative:

KroneckerDelta is neither convex nor concave:

First derivative with respect to :

Series expansion at a generic point:

Compute the indefinite integral using Integrate:

Verify the antiderivative:

More integrals: