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variants of this functions
Gamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[a,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/06.06.06.0028.01









  


  










Input Form





Gamma[a, z] == -((2 I Pi Floor[Arg[z - x]/(2 Pi)])/ (E^(I a Pi) Gamma[1 - a])) + Exp[2 Pi I a Floor[Arg[z - x]/(2 Pi)]] (Gamma[a, x] + Exp[-x] Sum[(((-1)^k Pochhammer[1 - a, j] x^(a - j - 1))/ (k j! (k - j - 1)!)) (z - x)^k, {k, 1, Infinity}, {j, 0, k - 1}]) /; Element[x, Reals] && x < 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List["a_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", "\[Pi]"]]], " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", "x"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", "a", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", "x"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", ",", "x"]], "]"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "x"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["k", "-", "1"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "a"]], ",", "j"]], "]"]], " ", SuperscriptBox["x", RowBox[List["a", "-", "j", "-", "1"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "x"]], ")"]], "k"]]], RowBox[List["k", " ", RowBox[List["j", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", "j", "-", "1"]], ")"]], "!"]]]]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "<", "0"]]]]]]]]]]










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





2007-05-02





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