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 Gamma

 http://functions.wolfram.com/06.05.04.0004.01

 Input Form

 Residue[Gamma[z], {z, -k}] == (-1)^k/k! /; Element[k, Integers] && k >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Residue", "[", RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], ",", RowBox[List["{", RowBox[List["z", ",", " ", RowBox[List["-", "k"]]]], "}"]]]], "]"]], " ", "\[Equal]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["k", "!"]]]]], " ", "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 res z ( Γ ( z ) ) ( - k ) ( - 1 ) k k ! /; k Condition Subscript res z Gamma z -1 k -1 k k -1 k [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Residue", "[", RowBox[List[RowBox[List["Gamma", "[", "z_", "]"]], ",", RowBox[List["{", RowBox[List["z_", ",", RowBox[List["-", "k_"]]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["k", "!"]]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29