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 LogGamma

 http://functions.wolfram.com/06.11.02.0001.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29