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 UnitStep

 http://functions.wolfram.com/14.01.09.0006.01

 Input Form

 UnitStep[x] == (1/2) (Limit[Erf[x/\[CurlyEpsilon]], \[CurlyEpsilon] -> Plus[0]] + 1)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Erf", "[", FractionBox["x", "\[CurlyEpsilon]"], "]"]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "+", "1"]], ")"]]]]]]]]

 MathML Form

 θ UnitStep ( x ) 1 2 ( lim ε "\[Rule]" + 0 erf ( x ε ) + 1 ) UnitStep x 1 2 ε ε 0 Erf x ε -1 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["UnitStep", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Erf", "[", FractionBox["x", "\[CurlyEpsilon]"], "]"]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "+", "1"]], ")"]]]]]]]]

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

 2001-10-29