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http://functions.wolfram.com/06.12.20.0008.01
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D[InverseGammaRegularized[a, z], {z, 6}] == E^(6 w) w^(1 - 6 a)
(1 - 120 a^5 + a^4 (274 + 600 w) - 3 a^3 (75 + 474 w + 400 w^2) +
a^2 (85 + 3 w (399 + 874 w + 400 w^2)) +
w (57 + 2 w (212 + w (437 + 60 w (5 + w)))) -
a (15 + 2 w (216 + w (923 + w (1037 + 300 w))))) Gamma[a]^6 /;
w == InverseGammaRegularized[a, z]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "6"]], "}"]]], RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["6", " ", "w"]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["6", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["120", " ", SuperscriptBox["a", "5"]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List["274", "+", RowBox[List["600", " ", "w"]]]], ")"]]]], "-", RowBox[List["3", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List["75", "+", RowBox[List["474", " ", "w"]], "+", RowBox[List["400", " ", SuperscriptBox["w", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["85", "+", RowBox[List["3", " ", "w", " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["874", " ", "w"]], "+", RowBox[List["400", " ", SuperscriptBox["w", "2"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["57", "+", RowBox[List["2", " ", "w", " ", RowBox[List["(", RowBox[List["212", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["437", "+", RowBox[List["60", " ", "w", " ", RowBox[List["(", RowBox[List["5", "+", "w"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["2", " ", "w", " ", RowBox[List["(", RowBox[List["216", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["923", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["1037", "+", RowBox[List["300", " ", "w"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", "a", "]"]], "6"]]]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]]]]]]]]
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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> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mn> 6 </mn> </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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> </mfrac> <mo>  </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 120 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 600 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 274 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 474 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 75 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 874 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 399 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 85 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 300 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 1037 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 923 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 216 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 437 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 212 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 57 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> w </mi> <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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 6 </cn> </degree> </bvar> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> w </ci> </apply> </apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -120 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 600 </cn> <ci> w </ci> </apply> <cn type='integer'> 274 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 474 </cn> <ci> w </ci> </apply> <cn type='integer'> 75 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 874 </cn> <ci> w </ci> </apply> <cn type='integer'> 399 </cn> </apply> </apply> <cn type='integer'> 85 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 300 </cn> <ci> w </ci> </apply> <cn type='integer'> 1037 </cn> </apply> </apply> <cn type='integer'> 923 </cn> </apply> </apply> <cn type='integer'> 216 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> w </ci> <apply> <plus /> <apply> <times /> <ci> w </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <ci> w </ci> <apply> <plus /> <ci> w </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> 437 </cn> </apply> </apply> <cn type='integer'> 212 </cn> </apply> </apply> <cn type='integer'> 57 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <eq /> <ci> w </ci> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "6"]], "}"]]]]], RowBox[List["InverseGammaRegularized", "[", RowBox[List["a_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["6", " ", "w"]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["6", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["120", " ", SuperscriptBox["a", "5"]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List["274", "+", RowBox[List["600", " ", "w"]]]], ")"]]]], "-", RowBox[List["3", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List["75", "+", RowBox[List["474", " ", "w"]], "+", RowBox[List["400", " ", SuperscriptBox["w", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["85", "+", RowBox[List["3", " ", "w", " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["874", " ", "w"]], "+", RowBox[List["400", " ", SuperscriptBox["w", "2"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["57", "+", RowBox[List["2", " ", "w", " ", RowBox[List["(", RowBox[List["212", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["437", "+", RowBox[List["60", " ", "w", " ", RowBox[List["(", RowBox[List["5", "+", "w"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["2", " ", "w", " ", RowBox[List["(", RowBox[List["216", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["923", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["1037", "+", RowBox[List["300", " ", "w"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", "a", "]"]], "6"]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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