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 LogGamma

 http://functions.wolfram.com/06.11.09.0001.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[RowBox[List["z", " ", RowBox[List["Log", "[", "n", "]"]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox["z", "k"]]], "]"]]]]]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "-", RowBox[List["Log", "[", "z", "]"]]]]]]]]

 MathML Form

 logΓ ( z ) lim n "\[Rule]" ( z log ( n ) - k = 1 n log ( 1 + z k ) ) - log ( z ) logΓ z n n z n -1 k 1 n 1 z k -1 -1 z [/itex]

 Rule Form

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

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

 2001-10-29