Editing Dirac delta function (section)

==Relationship to the Kronecker delta==
The [[Kronecker delta]] {{mvar|δ<sub>ij</sub>}} is the quantity defined by

<math display="block">\delta_{ij} = \begin{cases} 1 & i=j\\ 0 &i\not=j \end{cases} </math>

for all integers {{mvar|i}}, {{mvar|j}}.  This function then satisfies the following analog of the sifting property: if {{mvar|a<sub>i</sub>}} (for {{mvar|i}} in the set of all integers) is any [[Infinite sequence#Doubly-infinite sequences|doubly infinite sequence]], then

<math display="block">\sum_{i=-\infty}^\infty a_i \delta_{ik}=a_k.</math>

Similarly, for any real or complex valued continuous function {{mvar|f}} on {{math|'''R'''}}, the Dirac delta satisfies the sifting property

<math display="block">\int_{-\infty}^\infty f(x)\delta(x-x_0)\,dx=f(x_0).</math>

This exhibits the Kronecker delta function as a discrete analog of the Dirac delta function.{{sfn|Hartmann|1997|loc=pp. 154–155}}