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Er:Re: Er:Re: Er:Re: [Bug-gsl] discontinuity in dilog function
Gerard Jungman writes:
> 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.
I think this would be nicer. It would also then agree with the
definition in Maple and Abramowitz and Stegun.
Jim
>
> --
> Gerard Jungman <jungman@lanl.gov>
> Los Alamos National Laboratory
>
>
--
Dr. Jim McElwaine
H0.15, Department of Applied Maths and Theoretical Physics
Centre for Mathematical Sciences, Cambridge University
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