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Delta Function

Illustration

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Alternate names

Dirac delta function | Dirac distribution

Basic definition

The delta function, also called the Dirac delta function, is a generalized function that has the property that its convolution with any function f equals the value of f at zero.

Detailed definition

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" or the "impulse symbol". It is implemented in the Wolfram Language as DiracDelta[x]. Formally, δ is a linear functional from a space (commonly taken as a Schwartz space S or the space of all smooth functions of compact support D) of test functions f. The action of δ on f, commonly denoted δ[f] or ⟨δ, f⟩, then gives the value at 0 of f for any function f. In engineering contexts, the functional nature of the delta function is often suppressed.

Related terms

delta sequence | doublet function | generalized function | impulse symbol | Poincaré-Bertrand theorem | shah function | Sokhotsky's formula

Related Wolfram Language symbol

DiracDelta

Educational grade level

college level

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