EllipticE, limit x->1 ???

• To: mathgroup at smc.vnet.net
• Subject: [mg22360] EllipticE, limit x->1 ???
• From: bergervo at prl.philips.nl (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 wolfram.com

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?

Jos

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

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