Dirac Delta Functions

Functions > Symbolic Functions > Dirac Delta Functions

• Δ(x)—Returns the Dirac delta (Unit Impulse) function, which is defined as follows:

<region id="ID0EZVMCB" actualWidth="66.353333333333339" actualHeight="25.6" top="19.200000000000003" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="5"> <apply xmlns="http://schemas.mathsoft.com/math50"> <equal /> <apply> <id xml:space="preserve">Δ</id> <id xml:space="preserve">x</id> </apply> <real>0</real> </apply> </math> </region>	if	<region id="ID0E2WMCB" actualWidth="37.176666666666662" actualHeight="25.6" top="19.200000000000003" left="230.40000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="6"> <apply xmlns="http://schemas.mathsoft.com/math50"> <notEqual /> <id xml:space="preserve">x</id> <real>0</real> </apply> </math> </region>
and
<region id="ID0EYYMCB" actualWidth="104.39833333333335" actualHeight="56.800000000000004" top="76.800000000000011" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="7"> <apply xmlns="http://schemas.mathsoft.com/math50"> <equal /> <apply> <integral /> <lambda> <boundVars> <id xml:space="preserve">x</id> </boundVars> <apply> <id xml:space="preserve">Δ</id> <id xml:space="preserve">x</id> </apply> </lambda> <lowerBound> <apply> <neg /> <id xml:space="preserve">∞</id> </apply> </lowerBound> <upperBound> <id xml:space="preserve">∞</id> </upperBound> </apply> <real>1</real> </apply> </math> </region>

• Δ(n, x)—Returns the nth derivative of the Dirac delta function, which is defined as follows:

Δ(x) relates to Δ(n, x) as follows:

Arguments

• x is a real scalar.

• n is a nonnegative integer.