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http://functions.wolfram.com/09.54.16.0006.01
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ArithmeticGeometricMean[1, (2 Sqrt[b])/(1 + b)] ==
(2/(b + 1)) ArithmeticGeometricMean[1, b]
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Cell[BoxData[RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["1", ",", FractionBox[RowBox[List["2", SqrtBox["b"]]], RowBox[List["1", "+", "b"]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["2", RowBox[List["b", "+", "1"]]], RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["1", ",", "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> <semantics> <mi> agm </mi> <annotation-xml encoding='MathML-Content'> <ci> ArithmeticGeometricMean </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> b </mi> </msqrt> </mrow> <mrow> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mtext> </mtext> </mrow> <mrow> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <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> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ArithmeticGeometricMean </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ArithmeticGeometricMean </ci> <cn type='integer'> 1 </cn> <ci> b </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["1", ",", FractionBox[RowBox[List["2", " ", SqrtBox["b_"]]], RowBox[List["1", "+", "b_"]]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["1", ",", "b"]], "]"]]]], RowBox[List["b", "+", "1"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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