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 Gamma

 http://functions.wolfram.com/06.06.06.0002.01

 Input Form

 Gamma[a, z] == Gamma[a] - z^a Sum[(-z)^k/((a + k) k!), {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], "-", RowBox[List[SuperscriptBox["z", "a"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], "k"], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "k"]], ")"]], " ", RowBox[List["k", "!"]]]]]]]]]]]]]]]

 MathML Form

 Γ ( a , z ) Γ ( a ) - z a k = 0 ( - z ) k ( a + k ) k ! Gamma a z Gamma a -1 z a k 0 -1 z k a k k -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List["a_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], "-", RowBox[List[SuperscriptBox["z", "a"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], "k"], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "k"]], ")"]], " ", RowBox[List["k", "!"]]]]]]]]]]]]]]]

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

 2001-10-29