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 FractionalPart

 http://functions.wolfram.com/04.05.22.0004.01

 Input Form

 LaplaceTransform[FractionalPart[t], t, z] == (1/z^2) (1 - z/(E^z - 1)) /; Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaplaceTransform", "[", RowBox[List[RowBox[List["FractionalPart", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox["z", "2"]], RowBox[List["(", RowBox[List["1", "-", FractionBox["z", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 t [ frac ( t ) ] ( z ) 1 z 2 ( 1 - z z - 1 ) /; Re ( z ) > 0 Condition LaplaceTransform FractionalPart t t z 1 z 2 -1 1 -1 z z -1 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaplaceTransform", "[", RowBox[List[RowBox[List["FractionalPart", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["1", "-", FractionBox["z", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], "-", "1"]]]]], SuperscriptBox["z", "2"]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2001-10-29