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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/09.42.20.0012.01









  


  










Input Form





D[InverseJacobiDS[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) (-15 (-1 + m)^3 InverseJacobiDS[z, m] + ((-z) (-1 + m + z^2)^3 (m + z^2) ((8 + 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiDS[z, m], m], m] + (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[InverseJacobiDS[z, m], m], m]) + m z JacobiCN[InverseJacobiDS[z, m], m] ((-(-1 + m)) m z ((-1 + m) m (-2 + 5 m) + (1 + m (-7 + 8 m)) z^2 + (-1 + 3 m) z^4) - (-1 + m) (-1 + m + z^2) Sqrt[z^2/(m + z^2)] ((-1 + m) m (-7 + 12 m) + (4 + m (-19 + 18 m)) z^2 + (-3 + 5 m) z^4 - z^6) JacobiSN[InverseJacobiDS[z, m], m] + JacobiDN[InverseJacobiDS[z, m], m] (((-1 + m)^2 m z (-1 + m + z^2))/ Sqrt[z^2/(m + z^2)] + ((-1 + m)^2 m^2 (9 + m (-29 + 38 m)) + (-1 + m) m (-11 + m (66 + m (-152 + 119 m))) z^2 + (5 + m (-46 + m (158 + m (-248 + 139 m)))) z^4 + (-10 + m (47 + m (-94 + 73 m))) z^6 + (5 + 3 m (-4 + 5 m)) z^8) JacobiSN[InverseJacobiDS[z, m], m])))/(z (-1 + m + z^2)^3 (m + z^2)))










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)





2007-05-02





© 1998- Wolfram Research, Inc.