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variants of this functions
EllipticE






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z,m] > Series representations > Other series representations > Expansions E(sin-1(z)|m) at z==infinity





http://functions.wolfram.com/08.04.06.0084.01









  


  










Input Form





EllipticE[ArcSin[z], m] == -((Sqrt[1 - z^2] Sqrt[1 - m z^2])/z) + ((Sqrt[-z^2] Sqrt[-m])/(2 z)) ((((I Sqrt[-z^2])/Sqrt[z^2]) (Sqrt[1/m] - 1/Sqrt[m]) - Sqrt[1/m] - 1/Sqrt[m]) EllipticE[m] + 2 EllipticE[1/m] + 2 ((1 - m)/m) EllipticK[1/m] + 2 I (1 - Sqrt[m/(m - 1)] Sqrt[(m - 1)/m]) (-EllipticE[1 - 1/m] + (1/m) EllipticK[1 - 1/m])) + ((Sqrt[m] Sqrt[1 - 1/(m z^2)] Sqrt[1 - z^2])/(Sqrt[1 - 1/z^2] Sqrt[1 - m z^2])) EllipticE[ArcSin[1/(Sqrt[m] z)], 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)





2007-05-02





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