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 ArithmeticGeometricMean

 http://functions.wolfram.com/09.54.26.0003.01

 Input Form

 ArithmeticGeometricMean[a, b] == (Pi (a + b))/(4 EllipticK[((a - b)/(a + b))^2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a", ",", "b"]], "]"]], "\[Equal]", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], RowBox[List["4", " ", RowBox[List["EllipticK", "[", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["a", "-", "b"]], RowBox[List["a", "+", "b"]]], ")"]], "2"], "]"]]]]]]]]]

 MathML Form

 agm ArithmeticGeometricMean ( a , b ) π ( a + b ) 4 K ( ( a - b a + b ) 2 ) ArithmeticGeometricMean a b a b 4 EllipticK a -1 b a b -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArithmeticGeometricMean", "[", RowBox[List["a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], RowBox[List["4", " ", RowBox[List["EllipticK", "[", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["a", "-", "b"]], RowBox[List["a", "+", "b"]]], ")"]], "2"], "]"]]]]]]]]]

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

 2001-10-29

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