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 DiracDelta

 http://functions.wolfram.com/14.03.09.0002.01

 Input Form

 DiracDelta[x] == Limit[1/(2 \[CurlyEpsilon])/E^(Abs[x]/\[CurlyEpsilon]), \[CurlyEpsilon] -> 0]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["2", "\[CurlyEpsilon]"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", " ", FractionBox[RowBox[List[" ", RowBox[List["Abs", "[", "x", "]"]]]], "\[CurlyEpsilon]"]]]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", "0"]]]], "]"]]]]]]

 MathML Form

 δ DiracDelta ( x ) lim ε "\[Rule]" 0 1 2 ε - "\[LeftBracketingBar]" x "\[RightBracketingBar]" ε DiracDelta x ε ε 0 1 2 ε -1 -1 x ε -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["Abs", "[", "x", "]"]], "\[CurlyEpsilon]"]]]], RowBox[List["2", " ", "\[CurlyEpsilon]"]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", "0"]]]], "]"]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29