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 LogGamma

 http://functions.wolfram.com/06.11.16.0007.01

 Input Form

 LogGamma[2 z] == LogGamma[z] + LogGamma[z + 1/2] + Log[2] (2 z - 1) - Log[Pi]/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", RowBox[List["2", " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["1", "2"]]], "]"]], "+", RowBox[List[RowBox[List["Log", "[", "2", "]"]], RowBox[List["(", RowBox[List[RowBox[List["2", "z"]], "-", "1"]], ")"]]]], "-", FractionBox[RowBox[List["Log", "[", "\[Pi]", "]"]], "2"]]]]]]]

 MathML Form

 logΓ ( 2 z ) logΓ ( z + 1 2 ) + logΓ ( z ) + ( 2 z - 1 ) log ( 2 ) - log ( π ) 2 LogGamma 2 z LogGamma z 1 2 logΓ z 2 z -1 2 -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", RowBox[List["2", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List["LogGamma", "[", RowBox[List["z", "+", FractionBox["1", "2"]]], "]"]], "+", RowBox[List[RowBox[List["Log", "[", "2", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z"]], "-", "1"]], ")"]]]], "-", FractionBox[RowBox[List["Log", "[", "\[Pi]", "]"]], "2"]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.