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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 at generic point z==z0 > For the function itself





http://functions.wolfram.com/06.06.06.0022.01









  


  








Input Form





Gamma[a, z] \[Proportional] -((2 I Pi Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[Subscript[z, 0]])/(2 Pi)])/(E^(I a Pi) Gamma[1 - a])) + (1/Subscript[z, 0])^(a Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Subscript[z, 0]^(a Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (Gamma[a, Subscript[z, 0]] - (Subscript[z, 0]^(-1 + a) (z - Subscript[z, 0]))/E^Subscript[z, 0] + ((1/2) Subscript[z, 0]^(-2 + a) (1 - a + Subscript[z, 0]) (z - Subscript[z, 0])^2)/E^Subscript[z, 0] + O[(z - Subscript[z, 0])^3])








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["-", 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", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["zz", "0"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["1", SubscriptBox["zz", "0"]], ")"]], RowBox[List["a", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SubsuperscriptBox["zz", "0", RowBox[List["a", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", ",", SubscriptBox["zz", "0"]]], "]"]], "-", RowBox[List[SubsuperscriptBox["zz", "0", RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SubscriptBox["zz", "0"]]]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SubsuperscriptBox["zz", "0", RowBox[List[RowBox[List["-", "2"]], "+", "a"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SubscriptBox["zz", "0"]]]], " ", RowBox[List["(", RowBox[List["1", "-", "a", "+", SubscriptBox["zz", "0"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], "3"]]], ")"]]]]]]]]]]


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





2007-05-02