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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,m] > Series representations > Generalized power series > Expansions at generic point m==m0 > For the function itself





http://functions.wolfram.com/08.03.06.0032.01









  


  










Input Form





EllipticPi[n, m] \[Proportional] EllipticPi[n, Subscript[m, 0]] + (1/(2 (n - Subscript[m, 0]))) (EllipticE[Subscript[m, 0]]/ (Subscript[m, 0] - 1) + EllipticPi[n, Subscript[m, 0]]) (m - Subscript[m, 0]) + (1/2) ((3/(4 (-n + Subscript[m, 0])^2)) EllipticPi[n, Subscript[m, 0]] + (1/(4 (-1 + Subscript[m, 0]) Subscript[m, 0] (-n + Subscript[m, 0]))) EllipticK[Subscript[m, 0]] + ((-n - (2 + n) Subscript[m, 0] + 4 Subscript[m, 0]^2)/ (4 (-1 + Subscript[m, 0])^2 Subscript[m, 0] (-n + Subscript[m, 0])^2)) EllipticE[Subscript[m, 0]]) (m - Subscript[m, 0])^2 + O[(m - Subscript[m, 0])^3]










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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