DiscreteDelta2

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Values at fixed points

Values at infinities

General characteristics

Domain and analyticity

δ((Subscript[n, 1]),(Subscript[n, 2]),…,(Subscript[n, m])) is a nonanalytical function defined on (ℚ^m). Its possible values are 0 and 1. The value 1 is taken in case all arguments are 0.

Symmetries and periodicities

Parity

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

Permutation symmetry

Periodicity

No periodicity

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 discrete delta function.

Representations through equivalent functions

History

– L. Kronecker (1866, 1903)

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