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http://functions.wolfram.com/09.54.04.0003.02
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ArithmeticGeometricMean[Conjugate[a], Conjugate[b]] ==
Conjugate[ArithmeticGeometricMean[a, b]] /;
!IntervalMemberQ[Interval[{-Infinity, 0}], a/b]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List[RowBox[List["Conjugate", "[", "a", "]"]], ",", RowBox[List["Conjugate", "[", "b", "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", "b"]], "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", FractionBox["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> <mrow> <semantics> <mi> agm </mi> <annotation-xml encoding='MathML-Content'> <ci> ArithmeticGeometricMean </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mover> <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> </mover> </mrow> <mo> /; </mo> <mrow> <mfrac> <mi> a </mi> <mi> b </mi> </mfrac> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <semantics> <mi> agm </mi> <annotation-xml encoding='MathML-Content'> <ci> ArithmeticGeometricMean </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mover> <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> </mover> </mrow> <mo> /; </mo> <mrow> <mfrac> <mi> a </mi> <mi> b </mi> </mfrac> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List[RowBox[List["Conjugate", "[", "a_", "]"]], ",", RowBox[List["Conjugate", "[", "b_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", "b"]], "]"]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", FractionBox["a", "b"]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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