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EllipticE, limit x->1 ???

  • To: mathgroup at
  • Subject: [mg22360] EllipticE, limit x->1 ???
  • From: bergervo at (Bergervoet J.R.M.)
  • Date: Fri, 25 Feb 2000 21:14:12 -0500 (EST)
  • Organization: Philips Research Laboratories Eindhoven, Netherlands
  • Sender: owner-wri-mathgroup at

I need a series expansion of a function containing EllipticE (and
K as well), but I don't get an answer for:
  Series[EllipticE[x], {x, 1, 1}]
  Limit[EllipticE[x], x->1, Direction->1]

whereas the limit is clearly 1, as can be seen from the plot:

  Plot[EllipticE[x], {x,0,1}]

Now if I use the following, which is equal to EllipticE[x]

  EEx = Pi ( HypergeometricPFQ[{-1/2, 1/2}, {2}, x]/2
            - x HypergeometricPFQ[{1/2, 3/2}, {3}, x]/16 )
then at once the problems disappear, and the answers are given!

  Series[EEx, {x, 1, 1}]
  Limit[EEx, x->1, Direction->1]

Would it be possible to make Mathematica see these result by
itself, without having to help it with the hypergeometrics?


  Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
  Philips Research Laboratories,             Eindhoven, The Netherlands
  Building WS01                                     FAX: +31-40-2742224
  E-mail: bergervo at    Phone: +31-40-2742403

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