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 EllipticK

 http://functions.wolfram.com/08.02.17.0004.01

 Input Form

 EllipticK[z] == (1/Sqrt[1 - z]) Conjugate[EllipticK[z/(z - 1)]] /; Element[z, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["Conjugate", "[", RowBox[List["EllipticK", "[", FractionBox["z", RowBox[List["z", "-", "1"]]], "]"]], "]"]]]]]], "/;", RowBox[List["z", "\[Element]", "Reals"]]]]]]

 MathML Form

 K ( z ) 1 1 - z K ( z z - 1 ) _ /; z TagBox["\[DoubleStruckCapitalR]", Function[List[], Reals]] Condition EllipticK z 1 1 -1 z 1 2 -1 OverBar EllipticK z z -1 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["Conjugate", "[", RowBox[List["EllipticK", "[", FractionBox["z", RowBox[List["z", "-", "1"]]], "]"]], "]"]], SqrtBox[RowBox[List["1", "-", "z"]]]], "/;", RowBox[List["z", "\[Element]", "Reals"]]]]]]]]

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

 2007-05-02