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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 at m==infinity





http://functions.wolfram.com/08.06.06.0099.01









  


  










Input Form





EllipticPi[n, z, m] == (-1)^Round[Re[z]/Pi] (Sqrt[m Sin[z]^2]/(2 m Sin[z])) (((m Pi)/(m - n)) Sum[(Pochhammer[1/2, k]^2/(m^k k!^2)) Hypergeometric2F1[1/2, 1, 1 + k, n/(n - m)], {k, 0, Infinity}] - ((2 m Sqrt[1 - m Sin[z]^2])/(m - n)) Sum[(Pochhammer[1/2, k]/(m^k k!)) AppellF1[1/2, 1/2 - k, 1, 3/2, 1 - m Sin[z]^2, (n (1 - m Sin[z]^2))/ (n - m)], {k, 0, Infinity}]) + 2 Round[Re[z]/Pi] EllipticPi[n, m]










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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