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EllipticF






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticF[z,m] > Series representations > Generalized power series > Expansions at z==infinity





http://functions.wolfram.com/08.05.06.0051.01









  


  










Input Form





EllipticF[z, m] \[Proportional] (-1)^Round[Re[z]/Pi] ((-(Sqrt[-Sin[z]^2]/Sin[z])) (EllipticK[1 - m] + (I/2) (1 - (I Sqrt[-Sin[z]^4])/Sin[z]^2) (1 - Sqrt[m] Sqrt[1/m]) EllipticK[m]) + (Sqrt[-Sin[z]^2]/(Sin[z] Sqrt[(-m) Sin[z]^2])) (1 + ((1 + m)/(6 m)) Csc[z]^2 + ((3 + 2 m + 3 m^2)/(40 m^2)) Csc[z]^4 + O[Csc[z]^6])) + 2 Round[Re[z]/Pi] EllipticK[m] /; (Abs[z] -> Infinity)










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