Generalized Functions

The Wolfram Language's symbolic character allows it to handle generalized functions or "distributions" as a direct extension of classical mathematical functions, and to represent integrals and integral transforms that cannot be expressed in terms of continuous functions.

(RefLink[DiracDelta, paclet:ref/DiracDelta]) — one-dimensional or multidimensional delta function

(RefLink[HeavisideTheta, paclet:ref/HeavisideTheta]) — Heaviside step function, 0 for x<0 and 1 for x>0

(RefLink[Integrate, paclet:ref/Integrate]), (RefLink[D, paclet:ref/D]) — integrals and derivatives of generalized functions

(RefLink[LaplaceTransform, paclet:ref/LaplaceTransform]), (RefLink[FourierTransform, paclet:ref/FourierTransform]) — integral transforms

(RefLink[Convolve, paclet:ref/Convolve]) — convolve generalized functions

(RefLink[FunctionExpand, paclet:ref/FunctionExpand]) — expand out generalized functions