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InverseJacobiDS






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.42.20.0006.01









  


  










Input Form





D[InverseJacobiDS[z, m], {m, 2}] == (1/(4 (-1 + m)^2 m^2)) ((-2 + 4 m) EllipticE[JacobiAmplitude[InverseJacobiDS[z, m], m], m] + (-1 + m) EllipticF[JacobiAmplitude[InverseJacobiDS[z, m], m], m] + (1/((m + z^2) (-1 + m + z^2)^2)) (3 (m + z^2) (1 + m^2 - z^2 + m (-2 + z^2))^2 InverseJacobiDS[z, m] + m JacobiCS[InverseJacobiDS[z, m], m] (Sqrt[z^2/(m + z^2)] (1 + m^2 - z^2 + m (-2 + z^2)) - (5 m^3 + z^2 - z^4 + m^2 (-7 + 8 z^2) + m (2 - 7 z^2 + 3 z^4)) JacobiDN[InverseJacobiDS[z, m], m])))










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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