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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Series representations > Other series representations > Other expansions





http://functions.wolfram.com/08.06.06.0007.01









  


  










Input Form





EllipticPi[n, z, m] == Sqrt[n/((n - 1) (m - n))] (EllipticF[z, m] (Sqrt[((n - 1) (m - n))/n] + ((2 I Pi)/EllipticK[m]) Sum[(EllipticNomeQ[m]^k/(1 - EllipticNomeQ[m]^(2 k))) Sin[(k Pi a)/EllipticK[m]], {k, 1, Infinity}]) - 2 I Sum[(EllipticNomeQ[m]^k/(k (1 - EllipticNomeQ[m]^(2 k)))) Sin[(k Pi a)/EllipticK[m]] Sin[(k Pi EllipticF[z, m])/EllipticK[m]], {k, 1, Infinity}]) /; a == InverseJacobiSN[Sqrt[n/m], m] && -1 <= n <= 1 && -1 <= m <= 1 && -(Pi/2) <= z <= Pi/2










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)





2001-10-29





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