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http://functions.wolfram.com/06.12.06.0002.01
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InverseGammaRegularized[a, z] \[Proportional]
(1 - a) ProductLog[-1, -((z^(1/(a - 1)) Gamma[a]^(1/(a - 1)))/(a - 1))] /;
(z -> 0)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "a"]], ")"]], " ", RowBox[List["ProductLog", "[", RowBox[List[RowBox[List["-", "1"]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", FractionBox["1", RowBox[List["a", "-", "1"]]]], " ", SuperscriptBox[RowBox[List["Gamma", "[", "a", "]"]], FractionBox["1", RowBox[List["a", "-", "1"]]]]]], RowBox[List["a", "-", "1"]]]]]]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]
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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> <mrow> <msup> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> W </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> z </mi> <mfrac> <mn> 1 </mn> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </msup> </mrow> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "a"]], ")"]], " ", RowBox[List["ProductLog", "[", RowBox[List[RowBox[List["-", "1"]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["z", FractionBox["1", RowBox[List["a", "-", "1"]]]], " ", SuperscriptBox[RowBox[List["Gamma", "[", "a", "]"]], FractionBox["1", RowBox[List["a", "-", "1"]]]]]], RowBox[List["a", "-", "1"]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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