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 Gamma

 http://functions.wolfram.com/06.05.16.0020.01

 Input Form

 Gamma[z + n]/Gamma[z] == Product[z + k, {k, 0, n - 1}] /; Element[n, Integers] && n > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["Gamma", "[", RowBox[List["z", "+", "n"]], "]"]], RowBox[List["Gamma", "[", "z", "]"]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List["(", RowBox[List["z", "+", "k"]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

 MathML Form

 Γ ( z + n ) Γ ( z ) k = 0 n - 1 ( z + k ) /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] + Condition Gamma z n Gamma z -1 k 0 n -1 z k n SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["Gamma", "[", RowBox[List["z_", "+", "n_"]], "]"]], RowBox[List["Gamma", "[", "z_", "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List["(", RowBox[List["z", "+", "k"]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

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

 2007-05-02