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 DiracDelta

 http://functions.wolfram.com/14.03.09.0005.01

 Input Form

 DiracDelta[x] == Limit[(1/(2 Pi)) (Sin[x (n + 1/2)]/Sin[x/2]), n -> Infinity]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["2", "\[Pi]"]]], FractionBox[RowBox[List["Sin", "[", " ", RowBox[List["x", RowBox[List["(", RowBox[List["n", "+", FractionBox["1", "2"]]], ")"]]]], "]"]], RowBox[List["Sin", "[", FractionBox["x", "2"], "]"]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]

 MathML Form

 δ DiracDelta ( x ) lim n "\[Rule]" 1 2 π sin ( x 2 ) sin ( x ( n + 1 2 ) ) DiracDelta x n n 1 2 x 2 -1 -1 x n 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["x", " ", RowBox[List["(", RowBox[List["n", "+", FractionBox["1", "2"]]], ")"]]]], "]"]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], " ", RowBox[List["Sin", "[", FractionBox["x", "2"], "]"]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]

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

 2001-10-29