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ArithmeticGeometricMean




Mathematica Notation

Traditional Notation









Elliptic Functions > ArithmeticGeometricMean[a,b] > Identities > Functional identities





http://functions.wolfram.com/09.54.17.0001.01









  


  








Input Form





ArithmeticGeometricMean[c a, c b] == c ArithmeticGeometricMean[a, b] /; c > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List[RowBox[List["c", " ", "a"]], ",", " ", RowBox[List["c", " ", "b"]]]], "]"]], "\[Equal]", RowBox[List["c", " ", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", " ", "b"]], "]"]]]]]], "/;", " ", RowBox[List["c", ">", "0"]]]]]]








MathML Form







<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> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> c </mi> <mo> &#8290; </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> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> c </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> ArithmeticGeometricMean </ci> <apply> <times /> <ci> c </ci> <ci> a </ci> </apply> <apply> <times /> <ci> c </ci> <ci> b </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ci> ArithmeticGeometricMean </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> <apply> <gt /> <ci> c </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List[RowBox[List["c_", " ", "a_"]], ",", RowBox[List["c_", " ", "b_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["c", " ", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", "b"]], "]"]]]], "/;", RowBox[List["c", ">", "0"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29