BranchPoints[ArithmeticGeometricMean[a, b], a/b] == {0, ComplexInfinity}

Cell[BoxData[RowBox[List[RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", "b"]], "]"]], ",", FractionBox["a", "b"]]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["0", ",", " ", "ComplexInfinity"]], "}"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#8492;&#119979; </mi> <mfrac> <mi> a </mi> <mi> b </mi> </mfrac> </msub> <mo> ( </mo> <mrow> <semantics> <mi> agm </mi> <annotation-xml encoding='MathML-Content'> <ci> ArithmeticGeometricMean </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8492;&#119979; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> ArithmeticGeometricMean </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> <list> <cn type='integer'> 0 </cn> <apply> <ci> OverTilde </ci> <infinity /> </apply> </list> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a_", ",", "b_"]], "]"]], ",", FractionBox["a_", "b_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List["0", ",", "ComplexInfinity"]], "}"]]]]]]

2001-10-29