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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/08.06.06.0006.01









  


  










Input Form





EllipticPi[n, z, m] == Sum[n^k (Sqrt[1 + m/n] - (Sqrt[Pi]/(2 Gamma[1/2 - k] (k + 1)!)) (m/n)^(k + 1) Hypergeometric2F1[1, k + 1/2, k + 2, -(m/n)]) ((Sqrt[Pi] Gamma[k + 1/2])/(2 k!) - Cos[z] Hypergeometric2F1[1/2, 1/2 - k, 3/2, Cos[z]^2]), {k, 0, Infinity}] /; Inequality[0, LessEqual, m, Less, 1] && Inequality[0, LessEqual, n, Less, 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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