Re: EllipticE, limit x->1 ???
- To: mathgroup at smc.vnet.net
- Subject: [mg22528] Re: EllipticE, limit x->1 ???
- From: Adam Ciarkowski <aciark at ippt.gov.pl>
- Date: Thu, 9 Mar 2000 03:24:18 -0500 (EST)
- References: <897fju$65g@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Bergervoet J.R.M." wrote:
> ... I don't get an answer for:
>
> Series[EllipticE[x], {x, 1, 1}]
> Limit[EllipticE[x], x->1, Direction->1] ...
The point x = 1 is not a regular point of EllipticE[x]. By
continuing this function analytically onto complex x + I y
plane it can be seen with
Plot3D[Re[EllipticE[x + I y]], {x, 0.5, 1.5}, {y, -0.5, 0.5}];
Plot3D[Im[EllipticE[x + I y]], {x, 0.5, 1.5}, {y, -0.5, 0.5}]
that x = 1, y = 0 is a branch point of this function. Hence
the problems met when expanding it in a power series around
x = 1.
In the case like this the limit can be sought with the help of:
Needs["Calculus`Limit`"]
Limit[EllipticE[x], x -> 1].
Adam