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 Factorial2

 http://functions.wolfram.com/06.02.16.0010.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29