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Re: I don't understand -- Matlab/Maple refused compute the Taylor expansion of this function?
Posted:
Sep 1, 2006 2:07 PM
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Robert Israel wrote:
> In article <1157052597.072155.300000@74g2000cwt.googlegroups.com>,
> Luna Moon <lunamoonmoon@gmail.com> wrote:
>
> >I found everything now is very complicated... I need time to digest
> >what you said. I have never heard about the "outside residue theorem"
> >and "branch cut not being a straight line". Regular complex analysis
> >class never taught me these stuffs... could you please recommend some
> >readings about what you've used in your great tricks? I found it
> >difficult to follow the a few lines here, I have to read more
> >extensively ...
>
> You might try e.g. Marsden and Hoffman, "Basic Complex Analysis".
> What I called the "outside residue theorem" is Proposition 4.2.4
> in that book.
>
> >For now I just have a quick question about the last statement you've
> >made: "it is not possible to do it with the residue theorem", then is
> >there still a way to evalute the contour?
>
> I don't see any way off-hand. Of course you could always use
> numerical integration.
>
Thanks a lot Robert! I have a question about the non-straight branch
cuts and branch points at the infinity.
Do you mean if I have two branch points at -i and -1/3i, I cannot just
specify my branch cut be a curve that connects the two points, instead
of letting the branch cut go straight to the infinity?
If I have three branch points, do I have a way to wrap all my branch
cuts inside a small region enclosing all these three branch points?
That's to say, I hope there is a way to restrict the trouble of handing
the branch cuts to within a small region...
Moreover, if I want to integrate
Integrate( (2-z^(-1))^(-sqrt(2)), z on a contour along |z|=1),
so there is a branch point z=1/2 inside the contour |z|=1, is there a
way to integrate it?
Thanks again!
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