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 Factorial2

 http://functions.wolfram.com/06.02.03.0005.01

 Input Form

 (2 k - 1)!! == (2^k/Sqrt[Pi]) Gamma[k + 1/2] /; Element[k, Integers] && k >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]], ")"]], "!!"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", "k"], " "]], SqrtBox["\[Pi]"]], RowBox[List["Gamma", "[", RowBox[List["k", "+", FractionBox["1", "2"]]], "]"]]]]]], "/;", " ", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 ( 2 k - 1 ) !! 2 k π Γ ( k + 1 2 ) /; k Condition Factorial2 2 k -1 2 k 1 2 -1 Gamma k 1 2 k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k_"]], "-", "1"]], ")"]], "!!"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", "k"], " ", RowBox[List["Gamma", "[", RowBox[List["k", "+", FractionBox["1", "2"]]], "]"]]]], SqrtBox["\[Pi]"]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29