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 DiracDelta

 http://functions.wolfram.com/14.03.06.0001.01

 Input Form

 DiracDelta[x] == (1/(2 Pi)) Sum[E^(I k x), {k, -Infinity, Infinity}] /; -Pi < x < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "\[Pi]"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "k", " ", "x"]]]]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", "x", "<", "\[Pi]"]]]]]]

 MathML Form

 δ DiracDelta ( x ) 1 2 π k = - k x /; - π < x < π Condition DiracDelta x 1 2 -1 k -1 k x -1 x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "k", " ", "x"]]]]], RowBox[List["2", " ", "\[Pi]"]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", "x", "<", "\[Pi]"]]]]]]]]

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

 2001-10-29