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ArithmeticGeometricMean




Mathematica Notation

Traditional Notation









Elliptic Functions > ArithmeticGeometricMean[a,b] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.54.13.0002.01









  


  








Input Form





ArithmeticGeometricMean[a, b] - a D[ArithmeticGeometricMean[a, b], a] - b D[ArithmeticGeometricMean[a, b], b] == 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", " ", "b"]], "]"]], "-", RowBox[List["a", " ", RowBox[List[SubscriptBox["\[PartialD]", "a"], RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", " ", "b"]], "]"]]]]]], "-", RowBox[List["b", " ", RowBox[List[SubscriptBox["\[PartialD]", "b"], RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", " ", "b"]], "]"]]]]]]]], "\[Equal]", "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> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </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> &#8706; </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </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> &#8706; </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> ArithmeticGeometricMean </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <partialdiff /> <bvar> <ci> a </ci> </bvar> <apply> <ci> ArithmeticGeometricMean </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <partialdiff /> <bvar> <ci> b </ci> </bvar> <apply> <ci> ArithmeticGeometricMean </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a_", ",", "b_"]], "]"]], "-", RowBox[List["a_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["a_"]]], RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a_", ",", "b_"]], "]"]]]]]], "-", RowBox[List["b_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["b_"]]], RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a_", ",", "b_"]], "]"]]]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]


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





2001-10-29