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http://functions.wolfram.com/09.54.17.0004.01
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ArithmeticGeometricMean[a, 2 - a] == ArithmeticGeometricMean[1,
Sqrt[a (2 - a)]]
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Cell[BoxData[RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", RowBox[List["2", "-", "a"]]]], "]"]], "\[Equal]", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["1", ",", SqrtBox[RowBox[List["a", RowBox[List["(", RowBox[List["2", "-", "a"]], ")"]]]]]]], "]"]]]]]]
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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> <semantics> <mi> agm </mi> <annotation-xml encoding='MathML-Content'> <ci> ArithmeticGeometricMean </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <semantics> <mi> agm </mi> <annotation-xml encoding='MathML-Content'> <ci> ArithmeticGeometricMean </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <msqrt> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ArithmeticGeometricMean </ci> <ci> a </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <ci> ArithmeticGeometricMean </ci> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a_", ",", RowBox[List["2", "-", "a_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["1", ",", SqrtBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["2", "-", "a"]], ")"]]]]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
