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 Cos

 http://functions.wolfram.com/01.07.22.0002.01

 Input Form

 InverseFourierTransform[Cos[t], t, z] == Sqrt[Pi/2] DiracDelta[-1 + z] + Sqrt[Pi/2] DiracDelta[1 + z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["InverseFourierTransform", "[", RowBox[List[RowBox[List["Cos", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], "]"]]]], "+", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", RowBox[List["1", "+", "z"]], "]"]]]]]]]]]]

 MathML Form

 t - 1 [ cos ( t ) ] ( z ) π 2 δ ( z - 1 ) + π 2 δ ( z + 1 ) InverseFourierTransform t t z 2 -1 1 2 δ z -1 2 -1 1 2 δ z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseFourierTransform", "[", RowBox[List[RowBox[List["Cos", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], "]"]]]], "+", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", RowBox[List["1", "+", "z"]], "]"]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.