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 Gamma

 http://functions.wolfram.com/06.05.17.0006.01

 Input Form

 Gamma[z] == (2^(2 z)/z) Product[(1/Sqrt[Pi]) Gamma[1/2 + z/2^k], {k, 1, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["2", RowBox[List["2", "z"]]], "z"], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[FractionBox["1", SqrtBox["\[Pi]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", FractionBox["z", SuperscriptBox["2", "k"]]]], "]"]]]]]]]]]]]]

 MathML Form

 Γ ( z ) 2 2 z z k = 1 1 π Γ ( z 2 k + 1 2 ) Gamma z 2 2 z z -1 k 1 1 1 2 -1 Gamma z 2 k -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", FractionBox["z", SuperscriptBox["2", "k"]]]], "]"]], SqrtBox["\[Pi]"]]]]]], "z"]]]]]

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

 2001-10-29