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 UnitStep

 http://functions.wolfram.com/14.01.09.0008.01

 Input Form

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

 Standard Form

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

 MathML Form

 θ UnitStep ( x ) 1 π lim ε "\[Rule]" + 0 Si ( π x ε ) + 1 2 UnitStep x 1 -1 ε ε 0 SinIntegral x ε -1 1 2 [/itex]

 Rule Form

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

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

 2001-10-29