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 DiracDelta

 http://functions.wolfram.com/14.03.09.0014.01

 Input Form

 DiracDelta[x] == Limit[((2 l + 1)!!/(2^(l + 1) l!)) (1 - z^2)^l, l -> Infinity]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "l"]], "+", "1"]], ")"]], "!!"]], RowBox[List[SuperscriptBox["2", RowBox[List["l", "+", "1"]]], RowBox[List["l", "!"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], "l"]]], ",", RowBox[List["l", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]

 MathML Form

 δ DiracDelta ( x ) lim ε "\[Rule]" ( 2 l + 1 ) !! 2 l + 1 l ! ( 1 - z 2 ) l DiracDelta x ε ε Factorial2 2 l 1 2 l 1 l -1 1 -1 z 2 l [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "l"]], "+", "1"]], ")"]], "!!"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], "l"]]], RowBox[List[SuperscriptBox["2", RowBox[List["l", "+", "1"]]], " ", RowBox[List["l", "!"]]]]], ",", RowBox[List["l", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]

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

 2007-05-02