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variants of this functions
InverseBetaRegularized




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseBetaRegularized[z1,z2,a,b] > Differentiation > Low-order differentiation > With respect to b





http://functions.wolfram.com/06.24.20.0006.01









  


  








Input Form





D[InverseBetaRegularized[Subscript[z, 1], Subscript[z, 2], a, b], b] == Beta[a, b] (1 - w)^(1 - b) w^(1 - a) ((-BetaRegularized[1 - Subscript[z, 1], b, a]) Log[1 - Subscript[z, 1]] + (1/(b^2 Beta[a, b])) ((-HypergeometricPFQ[{1 - a, b, b}, {1 + b, 1 + b}, 1 - w]) (1 - w)^b + HypergeometricPFQ[{1 - a, b, b}, {1 + b, 1 + b}, 1 - Subscript[z, 1]] (1 - Subscript[z, 1])^b) + (PolyGamma[b] - PolyGamma[a + b]) Subscript[z, 2] - Log[1 - w] (-1 + BetaRegularized[Subscript[z, 1], a, b] + Subscript[z, 2])) /; w == InverseBetaRegularized[Subscript[z, 1], Subscript[z, 2], a, b]








Standard Form





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MathML Form







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<mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> b </ci> </bvar> <apply> <ci> InverseBetaRegularized </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> <ci> a </ci> <ci> b </ci> </apply> </apply> <apply> <times /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29