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 Subfactorial

 http://functions.wolfram.com/06.42.07.0001.01

 Input Form

 Subfactorial[z] == Integrate[(t - 1)^z/E^t, {t, 0, Infinity}] /; Re[z] > -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Subfactorial", "[", "z", "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["t", "-", "1"]], ")"]], "z"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", RowBox[List["-", "1"]]]]]]]]

 MathML Form

 Subfactorial ( z ) 0 ( t - 1 ) z - t t /; Re ( z ) > - 1 Condition Subfactorial z t 0 t -1 z -1 t z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Subfactorial", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["t", "-", "1"]], ")"]], "z"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", RowBox[List["-", "1"]]]]]]]]]]

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

 2007-05-02