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 Factorial2

 http://functions.wolfram.com/06.02.16.0009.01

 Input Form

 (n - 2 m)!! == ((-1)^m n!!)/(2^m Pochhammer[-(n/2), m]) /; Element[m, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["n", "-", RowBox[List["2", "m"]]]], ")"]], "!!"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], SuperscriptBox["2", RowBox[List["-", "m"]]], RowBox[List["n", "!!"]]]], RowBox[List[" ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", "m"]], "]"]]]]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]

 MathML Form

 ( n - 2 m ) !! ( - 1 ) m 2 - m n !! ( - n 2 ) m TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["n", "2"]]], ")"]], "m"], Pochhammer] /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition Factorial2 n -1 2 m -1 m 2 -1 m Factorial2 n Pochhammer -1 n 2 -1 m -1 m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["(", RowBox[List["n_", "-", RowBox[List["2", " ", "m_"]]]], ")"]], "!!"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox["2", RowBox[List["-", "m"]]], " ", RowBox[List["n", "!!"]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], ",", "m"]], "]"]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]]]

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

 2001-10-29