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InverseJacobiSD






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiSD[z,m] > Integration > Indefinite integration > Involving only one direct function with respect to m





http://functions.wolfram.com/09.47.21.0002.01









  


  










Input Form





Integrate[InverseJacobiSD[z, m], m] == 2 I Sqrt[m - 1] (EllipticE[I ArcSinh[Sqrt[m - 1] z], m/(m - 1)] - EllipticF[I ArcSinh[Sqrt[m - 1] z], m/(m - 1)]) + (1/(z Sqrt[1 + (m - 1) z^2])) (-2 Sqrt[1 + (m - 1) z^2] + 2 Sqrt[1 + m z^2] + 2 (m - 1) z^2 Sqrt[1 + m z^2] - Sqrt[1 + (m - 1) z^2] Log[(1/4) (2 + (2 m - 1) z^2 + 2 Sqrt[1 + (m - 1) z^2] Sqrt[1 + m z^2])]) /; z > 0 && m > 0










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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