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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 z==csc-1(n1/2)+Pi u/;uZ





http://functions.wolfram.com/08.06.06.0078.01









  


  










Input Form





EllipticPi[n, z, m] \[Proportional] (-(1/(2 Sqrt[n - 1] Sqrt[(n - m)/n]))) Log[z - Subscript[z, 0]] + (Pi I Sqrt[1/n])/ (2 Sqrt[1 - 1/n] Sqrt[1 - m/n]) + ((m (4 - 3 n) + (-2 + n) n)/(4 Sqrt[-1 + n] (-m + n) Sqrt[n - 1] Sqrt[(n - m)/n])) (z - Subscript[z, 0]) (1 + O[z - Subscript[z, 0]]) /; (z -> Subscript[z, 0]) && Subscript[z, 0] == ArcCsc[Sqrt[n]] + 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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