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 FractionalPart

 http://functions.wolfram.com/04.05.20.0002.01

 Input Form

 D[FractionalPart[x], x] == x - Sum[KroneckerDelta[k, 0] DiracDelta[x - k], {k, -Infinity, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "x"], RowBox[List["FractionalPart", "[", "x", "]"]]]], "\[Equal]", RowBox[List["x", "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["k", ",", "0"]], "]"]], RowBox[List["DiracDelta", "[", RowBox[List["x", "-", "k"]], "]"]]]]]]]]]]]]

 MathML Form

 frac ( x ) x x - k = - δ KroneckerDelta k , 0 δ DiracDelta ( x - k ) x FractionalPart x x -1 k -1 KroneckerDelta k 0 DiracDelta x -1 k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["FractionalPart", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["x", "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["k", ",", "0"]], "]"]], " ", RowBox[List["DiracDelta", "[", RowBox[List["x", "-", "k"]], "]"]]]]]]]]]]]]

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

 2001-10-29