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 Factorial2

 http://functions.wolfram.com/06.02.27.0001.01

 Input Form

 n!! == 2^(n/2) (Pi/2)^((1/4) (Cos[Pi n] - 1)) (n/2)!

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["n", "!!"]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["n", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox["\[Pi]", "2"], ")"]], RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "n"]], "]"]], "-", "1"]], ")"]]]]], " ", RowBox[List[FractionBox["n", "2"], "!"]]]]]]]]

 MathML Form

 n !! 2 n / 2 ( π 2 ) 1 4 ( cos ( π n ) - 1 ) n 2 ! Factorial2 n 2 n 2 -1 2 -1 1 4 n -1 n 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["n_", "!!"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["n", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox["\[Pi]", "2"], ")"]], RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "n"]], "]"]], "-", "1"]], ")"]]]]], " ", RowBox[List[FractionBox["n", "2"], "!"]]]]]]]]

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

 2001-10-29