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InverseJacobiNS






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiNS[z,m] > Differentiation > Low-order differentiation > With respect to m





http://functions.wolfram.com/09.45.20.0013.01









  


  










Input Form





D[InverseJacobiNS[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiNS[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiNS[z, m], m], m] + (1/(m - z^2)^3) (-15 (-1 + m)^3 (m - z^2)^3 InverseJacobiNS[z, m] + m z ((1/z^2) ((m - z^2) (m^2 (9 + m (-24 + 23 m)) - m (11 + 5 m (-6 + 7 m)) z^2 + (5 + 3 m (-4 + 5 m)) z^4) JacobiCD[InverseJacobiNS[z, m], m]) - (-1 + m) Sqrt[1 - m/z^2] (m - z^2)^2 JacobiCN[InverseJacobiNS[z, m], m])))










Standard Form





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MathML Form







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InverseJacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -23 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> </apply> <cn type='integer'> -8 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <ci> InverseJacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> m </ci> </apply> <cn type='integer'> -7 </cn> </apply> <apply> <ci> EllipticF </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <ci> InverseJacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> m </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> m </ci> <apply> <times /> 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type='integer'> 2 </cn> </apply> <apply> <ci> JacobiCN </ci> <apply> <ci> InverseJacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ci> InverseJacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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