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    Delta Function

    Illustration

    Illustration

    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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