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InverseJacobiCN






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.38.27.0018.01









  


  










Input Form





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










Standard Form





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MathML Form







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</mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> <mo> , </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> </mrow> <mo> , </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> } </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> &#10869; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox[SubsuperscriptBox["zz", "2", "2"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]], "+", RowBox[List["EllipticK", "[", RowBox[List["1", "-", FractionBox["1", "m"]]], "]"]]]], ")"]]]], RowBox[List[SubscriptBox["zz", "2"], " ", SqrtBox["m"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["a", ",", "b", ",", SubscriptBox["zz", "1"]]], "}"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "m"], "-", "2"]], ",", RowBox[List["1", "-", FractionBox["1", "m"]]], ",", 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["0", "<", "m", "<", "1"]]]]]]]]]]










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





2001-10-29





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