RamificationIndex[BetaRegularized[z, a, b], z, 1] == Log /; !Element[b, Integers] && !Element[b, Rationals]

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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> <mrow> <msub> <mi> &#8475; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mi> log </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mtext> &#8203; </mtext> <mrow> <mi> b </mi> <mo> &#8713; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8475; </ci> <ci> z </ci> </apply> <apply> <ci> BetaRegularized </ci> <ci> z </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 1 </cn> </apply> <ci> log </ci> </apply> <apply> <and /> <apply> <notin /> <ci> b </ci> <integers /> </apply> <apply> <notin /> <ci> b </ci> <rationals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["BetaRegularized", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], ",", "z_", ",", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "/;", RowBox[List[RowBox[List["!", RowBox[List["b", "\[Element]", "Integers"]]]], "&&", RowBox[List["!", RowBox[List["b", "\[Element]", "Rationals"]]]]]]]]]]]]

2001-10-29