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http://functions.wolfram.com/06.06.06.0037.01
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Gamma[-2, z] \[Proportional] (-(1/2)) Log[z] + 1/(2 z^2) - 1/z + 3/4 -
EulerGamma + z/6 - z^2/48 + z^3/360 + O[z^4]
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Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "2"]], ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], RowBox[List["Log", "[", "z", "]"]]]], "+", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox["1", "z"], "+", FractionBox["3", "4"], "-", "EulerGamma", "+", FractionBox["z", "6"], "-", FractionBox[SuperscriptBox["z", "2"], "48"], "+", FractionBox[SuperscriptBox["z", "3"], "360"], "+", RowBox[List["O", "[", SuperscriptBox["z", "4"], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> - </mo> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> z </mi> <mn> 6 </mn> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 48 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mn> 360 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Gamma </ci> <cn type='integer'> -2 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <eulergamma /> </apply> <cn type='rational'> 3 <sep /> 4 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 48 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 360 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "2"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Log", "[", "z", "]"]], "2"]]], "+", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox["1", "z"], "+", FractionBox["3", "4"], "-", "EulerGamma", "+", FractionBox["z", "6"], "-", FractionBox[SuperscriptBox["z", "2"], "48"], "+", FractionBox[SuperscriptBox["z", "3"], "360"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "4"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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