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InverseJacobiCN






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.38.27.0019.01









  


  










Input Form





InverseJacobiCN[z, m] == ((Sqrt[1 - z^2] JacobiDS[InverseJacobiCN[z, m], m])/ Sqrt[1 + m (-1 + z^2)]) ((-(Sqrt[(-1 + m - m z^2)/(-1 + m)]/Sqrt[1 - m + m z^2])) EllipticF[ArcSin[z], m/(-1 + m)] + Sqrt[1/(1 - m)] EllipticK[m/(-1 + m)]) /; !Exists[\[Tau], {Element[\[Tau], Reals], 0 < \[Tau] < 1}, Im[1 - (1 + \[Tau] (z - 1))^2] == 0 && 1 - (1 + \[Tau] (z - 1))^2 < 0 && Im[m (1 + \[Tau] (z - 1))^2 - m + 1] == 0 && m (1 + \[Tau] (z - 1))^2 - m + 1 < 0]










Standard Form





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MathML Form







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</ci> </bvar> <bvar> <list> <apply> <in /> <ci> &#964; </ci> <reals /> </apply> <apply> <lt /> <cn type='integer'> 0 </cn> <ci> &#964; </ci> <cn type='integer'> 1 </cn> </apply> </list> </bvar> <apply> <and /> <apply> <eq /> <apply> <imaginary /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <ci> &#964; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <ci> &#964; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <imaginary /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <ci> &#964; 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Rule Form





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





2007-05-02





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