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 Ceiling

 http://functions.wolfram.com/04.02.22.0002.01

 Input Form

 FourierCosTransform[Ceiling[t], t, z] == Sqrt[Pi/2] DiracDelta[z] - (1/(Sqrt[2 Pi] z)) Cot[z/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["FourierCosTransform", "[", RowBox[List[RowBox[List["Ceiling", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", "z", "]"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", "z"]]], RowBox[List["Cot", "[", FractionBox["z", "2"], "]"]]]]]]]]]]

 MathML Form

 ℱ𝒸 t [ t ] ( z ) π 2 δ DiracDelta ( z ) - 1 2 π z cot ( z 2 ) Subscript ℱ𝒸 t t z 2 -1 1 2 DiracDelta z -1 1 2 1 2 z -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierCosTransform", "[", RowBox[List[RowBox[List["Ceiling", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", "z", "]"]]]], "-", FractionBox[RowBox[List["Cot", "[", FractionBox["z", "2"], "]"]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", "z"]]]]]]]]]

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

 2001-10-29