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 EllipticK

 http://functions.wolfram.com/08.02.17.0003.01

 Input Form

 EllipticK[z] == (2/(1 + Sqrt[1 - z])) EllipticK[((1 - Sqrt[1 - z])/(1 + Sqrt[1 - z]))^2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticK", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", " "]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], RowBox[List["EllipticK", "[", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]], "2"], "]"]]]]]]]]

 MathML Form

 K ( z ) 2 1 + 1 - z K ( ( 1 - 1 - z 1 + 1 - z ) 2 ) EllipticK z 2 1 1 -1 z 1 2 -1 EllipticK 1 -1 1 -1 z 1 2 1 1 -1 z 1 2 -1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["EllipticK", "[", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], ")"]], "2"], "]"]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]

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

 2001-10-29