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 Factorial2

 http://functions.wolfram.com/06.02.02.0001.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29