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http://functions.wolfram.com/06.21.13.0006.01
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Wronskian[h[z], h[z] BetaRegularized[g[z], a, b], z] ==
((1 - g[z])^(-1 + b) g[z]^(-1 + a) h[z]^2 Derivative[1][g][z])/Beta[a, b]
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["h", "[", "z", "]"]], ",", RowBox[List[RowBox[List["h", "[", "z", "]"]], RowBox[List["BetaRegularized", "[", RowBox[List[RowBox[List["g", "[", "z", "]"]], ",", "a", ",", "b"]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["g", "[", "z", "]"]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], " ", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], " ", SuperscriptBox[RowBox[List["h", "[", "z", "]"]], "2"], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]]]]]
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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> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> h </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mrow> <mi> h </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mi> g </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mi> h </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> g </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <ci> h </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> h </ci> <ci> z </ci> </apply> <apply> <ci> BetaRegularized </ci> <apply> <ci> g </ci> <ci> z </ci> </apply> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> g </ci> <ci> z </ci> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> h </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["h", "[", "z_", "]"]], ",", RowBox[List[RowBox[List["h", "[", "z_", "]"]], " ", RowBox[List["BetaRegularized", "[", RowBox[List[RowBox[List["g", "[", "z_", "]"]], ",", "a_", ",", "b_"]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["g", "[", "z", "]"]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], " ", SuperscriptBox[RowBox[List["g", "[", "z", "]"]], RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], " ", SuperscriptBox[RowBox[List["h", "[", "z", "]"]], "2"], " ", RowBox[List[SuperscriptBox["g", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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