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InverseJacobiCS






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.39.20.0012.01









  


  










Input Form





D[InverseJacobiCS[z, m], {m, 3}] == (-(1/(4 (-1 + m)^3 m^3 (1 - m + z^2)^2))) ((1/2) (-1 + m - z^2) ((8 + 23 (-1 + m) m) (-1 + m - z^2) EllipticE[JacobiAmplitude[InverseJacobiCS[z, m], m], m] + (-1 + m) (m z Sqrt[1 - m/(1 + z^2)] + (-7 + 11 m) (-1 + m - z^2) EllipticF[JacobiAmplitude[InverseJacobiCS[z, m], m], m])) + (1/(2 (1 + z^2))) (15 (-1 + m)^3 (1 + z^2) (1 - m + z^2)^2 InverseJacobiCS[z, m] - m z ((-1 + m)^2 (5 + m (-13 + 23 m)) - 5 (-1 + m) (2 + m (-5 + 7 m)) z^2 + (5 + 3 m (-4 + 5 m)) z^4) JacobiND[InverseJacobiCS[z, m], m]))










Standard Form





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MathML Form







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<mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> cs </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> </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'> 3 </cn> </degree> </bvar> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </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> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> m </ci> <cn type='integer'> -1 </cn> </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> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> m </ci> </apply> <cn type='integer'> -7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> EllipticF </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <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> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> m </ci> </apply> <cn type='integer'> -4 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> m </ci> </apply> <cn type='integer'> -5 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 23 </cn> <ci> m </ci> </apply> <cn type='integer'> -13 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <ci> JacobiND </ci> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> <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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