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http://functions.wolfram.com/06.13.20.0005.01
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D[InverseGammaRegularized[a, Subscript[z, 1], Subscript[z, 2]],
Subscript[z, 2]] == E^InverseGammaRegularized[a, Subscript[z, 1],
Subscript[z, 2]] Gamma[a] InverseGammaRegularized[a, Subscript[z, 1],
Subscript[z, 2]]^(1 - a)
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["z", "2"]], RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]]], " ", RowBox[List["Gamma", "[", "a", "]"]], " ", SuperscriptBox[RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], RowBox[List["1", "-", "a"]]]]]]]]]
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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> <mfrac> <mrow> <mo> ∂ </mo> <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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <msup> <mi> ⅇ </mi> <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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> D </ci> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["z_", "2"]]]], RowBox[List["InverseGammaRegularized", "[", RowBox[List["a_", ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "]"]]], " ", RowBox[List["Gamma", "[", "a", "]"]], " ", SuperscriptBox[RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "]"]], RowBox[List["1", "-", "a"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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