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 Quotient

 http://functions.wolfram.com/04.07.16.0007.01

 Input Form

 Quotient[I m, n] == I Quotient[m, n] - 1 + CharacteristicFunction[Im[m/n], Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Quotient", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m"]], ",", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]]]], "-", "1", "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], ",", "Integers"]], "]"]]]]]]]]

 MathML Form

 quotient ( m , n ) quotient ( m , n ) + χ ( Im ( m n ) ) - 1 quotient m n quotient m n Subscript χ m n -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Quotient", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m_"]], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Quotient", "[", RowBox[List["m", ",", "n"]], "]"]]]], "-", "1", "+", RowBox[List["CharacteristicFunction", "[", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], ",", "Integers"]], "]"]]]]]]]]

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

 2001-10-29