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 UnitStep

 http://functions.wolfram.com/14.01.22.0006.01

 Input Form

 FourierTransform[UnitStep[t]/E^t, t, x] == I/(Sqrt[2 Pi] (I + x))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["FourierTransform", "[", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], RowBox[List["UnitStep", "[", "t", "]"]]]], ",", "t", ",", "x"]], "]"]], "\[Equal]", FractionBox["\[ImaginaryI]", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", "x"]], ")"]]]]]]]]]

 MathML Form

 t [ - t θ UnitStep ( t ) ] ( x ) 2 π ( + x ) FourierTransform -1 t UnitStep t t x 2 1 2 x -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierTransform", "[", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]], " ", RowBox[List["UnitStep", "[", "t_", "]"]]]], ",", "t_", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["\[ImaginaryI]", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", "x"]], ")"]]]]]]]]]

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

 2007-05-02