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 Floor

 http://functions.wolfram.com/04.01.16.0007.01

 Input Form

 Floor[(-I) z] == (-I) Floor[z] - I (1 - CharacteristicFunction[Re[z], Integers])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["Floor", "[", "z", "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", "Integers"]], "]"]]]], ")"]]]]]]]]]]

 MathML Form

 - z - z - ( 1 - χ ( Re ( z ) ) ) -1 z -1 z -1 1 -1 Subscript χ z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Floor", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["Floor", "[", "z", "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", "Integers"]], "]"]]]], ")"]]]]]]]]]]

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

 2001-10-29