DiracDelta2

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

General characteristics

Domain and analyticity

δ((Subscript[x, 1]),(Subscript[x, 2]),…) is a nonanalytical function; it is a generalized function defined for (Subscript[x, k])∈ℝ.

Symmetries and periodicities

Parity

δ((Subscript[x, 1]),(Subscript[x, 2]),…) is an even generalized function.

Permutation symmetry

Periodicity

No periodicity

Integral representations

On the real axis

Of the direct function

Differentiation

Symbolic differentiation

With respect to (Subscript[x, n])

In a distributional sense, for (Subscript[x, k])∈ℝ:

Integration

Definite integration

Multiple integration

Integral transforms

Fourier exp transforms

Inverse Fourier exp transforms

Fourier cos transforms

Fourier sin transforms

Laplace transforms

Representations through more general functions

Through Meijer G

Classical cases for the direct function itself

Representations through equivalent functions

Copyright