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 LogGamma

 http://functions.wolfram.com/06.11.16.0005.01

 Input Form

 LogGamma[z + n] == LogGamma[z] + Sum[Log[z + k], {k, 0, n - 1}] /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LogGamma", "[", RowBox[List["z", "+", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List["Log", "[", RowBox[List["z", "+", "k"]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 logΓ ( z + n ) logΓ ( z ) + k = 0 n - 1 log ( k + z ) /; n Condition LogGamma z n logΓ z k 0 n -1 k z n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LogGamma", "[", RowBox[List["z_", "+", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["LogGamma", "[", "z", "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List["Log", "[", RowBox[List["z", "+", "k"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29