KroneckerDelta2

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

Values at infinities

General characteristics

Domain and analyticity

(Subscript[δ, (Subscript[n, 1]),(Subscript[n, 2]),…,(Subscript[n, m])]) is a nonanalytical function defined over (ℚ^m). Its possible values are 0 and 1.

Symmetries and periodicities

Parity

(Subscript[δ, (Subscript[n, 1]),(Subscript[n, 2]),…,(Subscript[n, m])]) is an even function.

Permutation symmetry

Periodicity

No periodicity

Integral representations

On the real axis

Contour integral representations

Transformations

Transformations and argument simplifications

Products, sums, and powers of the direct function

Identities

Functional identities

Complex characteristics

Real part

Imaginary part

Absolute value

Argument

Conjugate value

Summation

Infinite summation

Above relation represents the sifting property of Kronecker delta function.

Representations through equivalent functions

History

– L. Kronecker (1866, 1903)

The function δ((Subscript[n, 1]),(Subscript[n, 2]),…,(Subscript[n, m])) is encountered often in mathematics and the natural sciences.

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