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 HeavisideTheta

 http://functions.wolfram.com/14.05.09.0005.01

 Input Form

 HeavisideTheta[x] == (1/Pi) Limit[ArcTan[x/\[CurlyEpsilon]], \[CurlyEpsilon] -> Plus[0]] + 1/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HeavisideTheta", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["1", " "]], "\[Pi]"], RowBox[List["Limit", "[", RowBox[List[RowBox[List["ArcTan", "[", FractionBox["x", "\[CurlyEpsilon]"], "]"]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]]]], "+", FractionBox["1", "2"]]]]]]]

 MathML Form

 θ HeavisideTheta ( x ) 1 π lim ε "\[Rule]" + 0 tan - 1 ( x ε ) + 1 2 HeavisideTheta x 1 -1 ε ε 0 x ε -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HeavisideTheta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["Limit", "[", RowBox[List[RowBox[List["ArcTan", "[", FractionBox["x", "\[CurlyEpsilon]"], "]"]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Pi]"], "+", FractionBox["1", "2"]]]]]]]

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

 2007-05-02