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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/08.05.06.0079.01









  


  










Input Form





EllipticF[ArcSin[z], m] \[Proportional] (-(Sqrt[-z^2]/z)) (EllipticK[1 - m] + (1/2) I (1 - Sqrt[1/m] Sqrt[m]) (1 - (I Sqrt[-z^4])/z^2) EllipticK[m]) - ((Sqrt[-z^2] Sqrt[(-m) z^2])/(m z^3)) (1 + (1 + m)/(6 m z^2) + (3 + 2 m + 3 m^2)/(40 m^2 z^4) + \[Ellipsis]) /; (Abs[z] -> Infinity)










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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