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 Factorial2

 http://functions.wolfram.com/06.02.08.0002.01

 Input Form

 (2 k - 1)!! == Product[2 j - 1, {j, 1, k}] /; 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[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "k"], RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "-", "1"]], ")"]]]]]], "/;", " ", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 ( 2 k - 1 ) !! j = 1 k ( 2 j - 1 ) /; k Condition Factorial2 2 k -1 j 1 k 2 j -1 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[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "k"], RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "-", "1"]], ")"]]]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29