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 UnitStep

 http://functions.wolfram.com/14.01.07.0004.01

 Input Form

 UnitStep[x] == (1/Pi) Limit[Integrate[(1/t) Sin[t/\[CurlyEpsilon]], {t, -Infinity, x}], \[CurlyEpsilon] -> Plus[0]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "\[Equal]", RowBox[List[FormBox[FractionBox["1", "\[Pi]"], TraditionalForm], RowBox[List["Limit", "[", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "x"], RowBox[List[FractionBox["1", "t"], RowBox[List["Sin", "[", FractionBox["t", "\[CurlyEpsilon]"], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]]]]]]]]

 MathML Form

 θ UnitStep ( x ) 1 π lim ε "\[Rule]" + 0 - x 1 t sin ( t ε ) t UnitStep x 1 -1 ε ε 0 t -1 x 1 t -1 t ε -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["UnitStep", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Limit", "[", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "x"], RowBox[List[FractionBox[RowBox[List["Sin", "[", FractionBox["t", "\[CurlyEpsilon]"], "]"]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]], ",", RowBox[List["\[CurlyEpsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Pi]"]]]]]

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

 2001-10-29