Subscript[z, 2] == BetaRegularized[Subscript[z, 1], w, a, b] /; w == InverseBetaRegularized[Subscript[z, 1], Subscript[z, 2], a, b]

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["z", "2"], "\[Equal]", RowBox[List["BetaRegularized", "[", RowBox[List[SubscriptBox["z", "1"], ",", "w", ",", "a", ",", "b"]], "]"]]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseBetaRegularized", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"], ",", "a", ",", "b"]], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mrow> <msub> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> w </mi> <mo> &#10869; </mo> <mrow> <msubsup> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <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> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> BetaRegularized </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <ci> w </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> <apply> <eq /> <ci> w </ci> <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> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["BetaRegularized", "[", RowBox[List[SubscriptBox["$Failed", "1"], ",", "w", ",", "a", ",", "b"]], "]"]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseBetaRegularized", "[", RowBox[List[SubscriptBox["$Failed", "1"], ",", SubscriptBox["$Failed", "2"], ",", "a", ",", "b"]], "]"]]]]]]]]]]

2001-10-29