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Re: Er:Re: Er:Re: [Bug-gsl] discontinuity in dilog function
- From: Gerard Jungman <jungman at lanl dot gov>
- To: Jim McElwaine <J dot N dot McElwaine at damtp dot cam dot ac dot uk>
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Tue, 21 Sep 2004 12:07:16 -0600
- Subject: Re: Er:Re: Er:Re: [Bug-gsl] discontinuity in dilog function
- Organization: Los Alamos National Laboratory
- References: <16705.59385.635354.443824@yuki.amtp.cam.ac.uk> <1095105715.12458.136.camel@bellerophon.lanl.gov> <16711.14100.301839.247520@yuki.amtp.cam.ac.uk> <1095451053.12458.228.camel@bellerophon.lanl.gov> <16719.57669.141666.794848@yuki.amtp.cam.ac.uk>
On Tue, 2004-09-21 at 02:07, Jim McElwaine wrote:
> I've attached two figures.
> Each contains dilog evaluated over |Re(z)|<2 |Im(z)|<2
> Each figure has four sub figures showing contours of
> abs(Li2), arg(Li2), Real(Li2), Imag(Li2)
> The first figure (1.png) has -\pi<arg(z)<\pi
> the second figure (2.png) calls dilog with pi<arg(z)<3*pi
> You can clearly see the discontinuities
Ok. I guess my tests missed again.
> My only point about the branch point was that since the argument is
> passed as re^{i\theta}, if the definition used is
> \int log(z)/(1-z) so the branch point is at the origin
> Then the function can be defined over the full Riemann surface using
> \theta and no branch cut is necessary.
Yes. Is this desirable?
My only concern is to avoid confusing people;
is this the way it is typically used? Anyway, it is
certainly more appealing to do it for the whole
Riemann surface, so I have an urge to just do it.
--
Gerard Jungman <jungman@lanl.gov>
Los Alamos National Laboratory