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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 m==1





http://functions.wolfram.com/08.03.06.0042.01









  


  








Input Form





EllipticPi[n, m] \[Proportional] (1/2) ((-Log[1 - m]) (1/(1 - n)) (1 + ((n + 1) (m - 1))/(4 (n - 1)) - (3 (-3 - 6 n + n^2) (m - 1)^2)/(64 (n - 1)^2) + \[Ellipsis]) + (-4 Log[2] + Sqrt[n] (-Log[1 - Sqrt[n]] + Log[1 + Sqrt[n]]))/(-1 + n) - ((-1 + 2 Log[2] + 2 n Log[2] + Sqrt[n] (Log[1 - Sqrt[n]] - Log[1 + Sqrt[n]]))/(2 (-1 + n)^2)) (m - 1) + (1/(64 (-1 + n)^3)) (21 + 12 n - 5 n^2 + 12 (-3 + (-6 + n) n) Log[2] + 24 Sqrt[n] (-Log[1 - Sqrt[n]] + Log[1 + Sqrt[n]])) (m - 1)^2 + \[Ellipsis]) /; (m -> 1)








Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02