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InverseJacobiND






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.44.20.0012.01









  


  










Input Form





D[InverseJacobiND[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiND[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiND[z, m], m], m] + (1/(z (1 + (-1 + m) z^2)^2)) (-15 (-1 + m)^3 z (1 + (-1 + m) z^2)^2 InverseJacobiND[z, m] + (m^4 z^4 (45 - 11 Sqrt[1/z^2] z) - (-15 + 7 Sqrt[1/z^2] z) (-1 + z^2)^2 + m (-1 + z^2) (40 - 17 Sqrt[1/z^2] z - 75 z^2 + 32 Sqrt[1/z^2] z^3) + m^3 z^2 (75 - 21 Sqrt[1/z^2] z - 135 z^2 + 40 Sqrt[1/z^2] z^3) + m^2 (33 - 10 Sqrt[1/z^2] z - 160 z^2 + 56 Sqrt[1/z^2] z^3 + 150 z^4 - 54 Sqrt[1/z^2] z^5)) JacobiSC[InverseJacobiND[z, m], m]))










Standard Form





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MathML Form







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<mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> nd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> nd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> m </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> InverseJacobiND </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 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</apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <cn type='integer'> 45 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <power /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z 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</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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