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 Ceiling

 http://functions.wolfram.com/04.02.27.0008.01

 Input Form

 Ceiling[z] == z + ArcTan[Cot[Pi z]]/Pi + 1/2 /; Element[z, Reals] && !Element[z, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Ceiling", "[", "z", "]"]], "\[Equal]", RowBox[List["z", "+", FractionBox[RowBox[List["ArcTan", "[", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "]"]], "\[Pi]"], "+", FractionBox["1", "2"]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["z", ",", "Reals"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["z", ",", "Integers"]], "]"]], "]"]]]]]]]]

 MathML Form

 z z + tan - 1 ( cot ( π z ) ) π + 1 2 /; z TagBox["\[DoubleStruckCapitalR]", Function[Reals]] z TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z z -1 1 2 z z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Ceiling", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", "+", FractionBox[RowBox[List["ArcTan", "[", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "]"]], "\[Pi]"], "+", FractionBox["1", "2"]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["!", RowBox[List["z", "\[Element]", "Integers"]]]]]]]]]]]]

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

 2001-10-29