Re: EllipticE, limit x->1 ???
- To: mathgroup at smc.vnet.net
- Subject: [mg22497] Re: EllipticE, limit x->1 ???
- From: Jos R Bergervoet <Jos.Bergervoet at philips.com>
- Date: Wed, 8 Mar 2000 02:22:38 -0500 (EST)
- Organization: Philips Research Laboratories
- Sender: owner-wri-mathgroup at wolfram.com
aciark at ippt.gov.pl wrote:
> (after I wrote:)
> > Series[EllipticE[x], {x, 1, 1}]
> > Limit[EllipticE[x], x->1, Direction->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!
>
> In the case like this the limit can be sought with the help of:
> Needs["Calculus`Limit`"]
> Limit[EllipticE[x], x -> 1].
OK, but for the Series this still doesn't solve it.
Would it be allowed to "replace" EllipticE[x] with another
function, which I define as:
Pi ( HypergeometricPFQ[{-1/2, 1/2}, {2}, x]/2
- x HypergeometricPFQ[{1/2, 3/2}, {3}, x]/16 )
I have an expression with several occurrences of EllipticE[], but
then of course for arguments other than 'x' as well.
NB: Acc. to FullSimplify[EllipticE[x] - EEx], the difference is 0,
Nevertheless, the expansions work for the latter only :-(
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