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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[a,z] > Continued fraction representations





http://functions.wolfram.com/06.06.10.0003.01









  


  








Input Form





Gamma[a, z] == z^a/(E^z (1 - a + z + (a - 1)/(3 - a + z + (2 (a - 2))/ (5 - a + z + (3 (a - 3))/(7 - a + z + (4 (a - 4))/ (9 - a + z + (5 (a - 5))/(11 - a + z + \[Ellipsis]))))))) /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]]]], RowBox[List["1", "-", "a", "+", "z", "+", FractionBox[RowBox[List["a", "-", "1"]], RowBox[List["3", "-", "a", "+", "z", "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["a", "-", "2"]], ")"]]]], RowBox[List["5", "-", "a", "+", "z", "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["a", "-", "3"]], ")"]]]], RowBox[List["7", "-", "a", "+", "z", "+", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["a", "-", "4"]], ")"]]]], RowBox[List["9", "-", "a", "+", "z", "+", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List["a", "-", "5"]], ")"]]]], RowBox[List["11", "-", "a", "+", "z", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]








MathML Form







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Rule Form





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





2001-10-29