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variants of this functions
EllipticPi




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Representations through more general functions > Through hypergeometric functions of two variables





http://functions.wolfram.com/08.06.26.0001.01









  


  








Input Form





EllipticPi[n, z, m] == (-1)^Round[Re[z]/Pi] Sum[(Sin[z]^(1 + 2 k)/(1 + 2 k)) AppellF1[1/2 + k, 1/2, 1/2, 3/2 + k, Sin[z]^2, m Sin[z]^2] n^k, {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)





2001-10-29