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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Series representations > Generalized power series > Expansions on branch cuts > Formulas on real axis for real m, n > For m<1<n,csc-1(n1/2)+Pi u<xu+1/2)/;uZ





http://functions.wolfram.com/08.06.06.0026.01









  


  










Input Form





EllipticPi[n, z, m] \[Proportional] EllipticPi[n, x, m] + ((Pi I Sqrt[n])/(2 Sqrt[n - 1] Sqrt[n - m])) (1 - Exp[(-Pi) I Floor[Arg[x - z]/(2 Pi)]]) + Exp[(-Pi) I Floor[Arg[x - z]/(2 Pi)]] ((1/(Sqrt[1 - m Sin[x]^2] (1 - n Sin[x]^2))) (z - x) - ((Sin[2 x] (-m - 2 n + 3 m n Sin[x]^2))/(4 (1 - m Sin[x]^2)^(3/2) (n Sin[x]^2 - 1)^2)) (z - x)^2 + \[Ellipsis]) /; (z -> x) && Element[x, Reals] && Element[m, Reals] && Element[n, Reals] && m < 1 < n && ArcCsc[Sqrt[n]] + Pi u < x < Pi/2 + Pi u && Element[u, Integers]










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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