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 LogGamma

 http://functions.wolfram.com/06.11.16.0006.01

 Input Form

 LogGamma[z - n] == LogGamma[z] - Sum[Log[z - k], {k, 1, n}] /; 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", "=", "1"]], "n"], 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 = 1 n log ( z - k ) /; n Condition LogGamma z -1 n logΓ z -1 k 1 n z -1 k 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", "=", "1"]], "n"], 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