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variants of this functions
EllipticE






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z,m] > Series representations > Generalized power series > Expansions at m==0





http://functions.wolfram.com/08.04.06.0006.01









  


  










Input Form





EllipticE[z, m] == (Pi/2) Sum[(Pochhammer[-(1/2), k] Pochhammer[1/2, k] m^k)/k!^2, {k, 0, Infinity}] - Cos[z] (Sum[((Pochhammer[-(1/2), j] Pochhammer[1/2, j] Pochhammer[1/2, k] (-m)^j)/((1 + 2 j + 2 k) (j + k)! j!)) Cos[z]^(2 j + 2 k), {j, 0, Infinity}, {k, 0, Infinity}] - (m/2) Sum[((Pochhammer[1/2, j + k] Pochhammer[3/2, j + k] (-1)^j m^(j + k))/((j + k + 1)! j! (2 j + 1) Pochhammer[3/2, k])) Cos[z]^(2 j), {j, 0, Infinity}, {k, 0, Infinity}])










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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