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 LogGamma

 http://functions.wolfram.com/06.11.06.0029.01

 Input Form

 LogGamma[z] == (-EulerGamma) z - Log[z] - Sum[Log[1 + z/k] - z/k, {k, 1, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "EulerGamma"]], " ", "z"]], "-", RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox["z", "k"]]], "]"]], "-", FractionBox["z", "k"]]], ")"]]]]]]]]]]

 MathML Form

 logΓ ( z ) - TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] z - log ( z ) - k = 1 ( log ( 1 + z k ) - z k ) LogGamma z -1 z -1 z -1 k 1 1 z k -1 -1 z k -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "EulerGamma"]], " ", "z"]], "-", RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox["z", "k"]]], "]"]], "-", FractionBox["z", "k"]]], ")"]]]]]]]]]]

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

 2007-05-02