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EllipticF




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.05.06.0082.01









  


  








Input Form





EllipticF[ArcSin[z], m] == (-(Sqrt[-z^2]/z)) (EllipticK[1 - m] + (I/2) (1 - (I Sqrt[-z^4])/z^2) (1 - Sqrt[m] Sqrt[1/m]) EllipticK[m]) - ((Sqrt[-z^2] Sqrt[(-m) z^2])/(m z^3)) Sum[((Pochhammer[1/2, k]/((2 k + 1) k!)) Hypergeometric2F1[1/2, -k, 1/2 - k, 1/m])/z^(2 k), {k, 0, Infinity}] /; Abs[z] > 1








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