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 FractionalPart

 http://functions.wolfram.com/04.05.16.0004.01

 Input Form

 FractionalPart[n + z] == FractionalPart[z] + UnitStep[n + z] - UnitStep[z] /; Element[n, Integers] && !Element[z, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["FractionalPart", "[", RowBox[List["n", "+", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["FractionalPart", "[", "z", "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List["n", "+", "z"]], "]"]], "-", RowBox[List["UnitStep", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["z", ",", "Integers"]], "]"]], "]"]]]]]]]]

 MathML Form

 frac ( n + z ) frac ( z ) + θ ( n + z ) - θ ( z ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] z TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition FractionalPart n z FractionalPart z θ n z -1 θ z n z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FractionalPart", "[", RowBox[List["n_", "+", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["FractionalPart", "[", "z", "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List["n", "+", "z"]], "]"]], "-", RowBox[List["UnitStep", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["!", RowBox[List["z", "\[Element]", "Integers"]]]]]]]]]]]]

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

 2001-10-29