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InverseJacobiNC






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiNC[z,m] > Representations through equivalent functions > With related functions > Involving other related functions





http://functions.wolfram.com/09.43.27.0015.01









  


  










Input Form





InverseJacobiNC[z, m] == (1/Sqrt[1 - m]) ((Sqrt[Subscript[z, 2]^2]/Subscript[z, 2]) EllipticLog[{Subscript[z, 1], Subscript[z, 2]}, {a, b}] - EllipticK[m/(m - 1)]) /; {a, b, Subscript[z, 1]} == {(2 m - 1)/(1 - m), m/(m - 1), z^2} && Subscript[z, 1]^3 + a Subscript[z, 1]^2 + b Subscript[z, 1] - Subscript[z, 2]^2 == 0 && 0 < z < 1 && m > 1










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiNC", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[FractionBox[RowBox[List[SqrtBox[SubsuperscriptBox["zz", "2", "2"]], " ", RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]]]], SubscriptBox["zz", "2"]], "-", RowBox[List["EllipticK", "[", FractionBox["m", RowBox[List["m", "-", "1"]]], "]"]]]], SqrtBox[RowBox[List["1", "-", "m"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["a", ",", "b", ",", SubscriptBox["zz", "1"]]], "}"]], "\[Equal]", RowBox[List["{", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", " ", "m"]], "-", "1"]], RowBox[List["1", "-", "m"]]], ",", FractionBox["m", RowBox[List["m", "-", "1"]]], ",", SuperscriptBox["z", "2"]]], "}"]]]], "&&", RowBox[List[RowBox[List[SubsuperscriptBox["zz", "1", "3"], "+", RowBox[List["a", " ", SubsuperscriptBox["zz", "1", "2"]]], "+", RowBox[List["b", " ", SubscriptBox["zz", "1"]]], "-", SubsuperscriptBox["zz", "2", "2"]]], "\[Equal]", "0"]], "&&", RowBox[List["0", "<", "z", "<", "1"]], "&&", RowBox[List["m", ">", "1"]]]]]]]]]]










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





2001-10-29





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