ArithmeticGeometricMean[1, b] \[Proportional] SeriesData[$CellContext`z, 0, {1, 0, Rational[1, 6] $CellContext`m, 0, Rational[1, 120] (-4 $CellContext`m + 9 $CellContext`m^2), 0, Rational[1, 5040] (16 $CellContext`m - 180 $CellContext`m^2 + 225 $CellContext`m^3), 0, Rational[1, 362880] (-64 $CellContext`m + 3024 $CellContext`m^2 - 12600 $CellContext`m^3 + 11025 $CellContext`m^4)}, 1, 11, 1] /; (b -> 1)

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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> <mn> 1 </mn> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> ArithmeticGeometricMean </ci> <cn type='integer'> 1 </cn> <ci> b </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29