EllipticPi[n, z, m] \[Proportional] (EllipticF[z, m] + ((-EllipticE[z, m] + EllipticF[z, m])/m) n - (1/(6 m^2)) (n^2 (4 (1 + m) EllipticE[z, m] - 2 ((2 + m) EllipticF[z, m] + m Cos[z] Sin[z] Sqrt[1 - m Sin[z]^2]))) + O[n^3]) + 2 Round[Re[z]/Pi] (EllipticK[m] - ((EllipticE[m] - EllipticK[m])/m) n - ((2 (1 + m) EllipticE[m] - (2 + m) EllipticK[m])/(3 m^2)) n^2 + O[n^3]) /; (n -> 0)

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2007-05-02