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Re: Discrepancy between Integrate and NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83671] Re: Discrepancy between Integrate and NIntegrate
  • From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Wed, 28 Nov 2007 05:26:36 -0500 (EST)
  • References: <figut3$fqd$1@smc.vnet.net>

chuck009 <dmilioto at comcast.com> wrote:
> >
> > If you have any further questions, let me know.

When I said that, I meant any further questions directly related to the
discrepancy you initially mentioned and the work-around which I then
provided.

Offhand, I don't know the answer to your question below. Perhaps someone
else can help you with it.

David

> Ok . . . I don't see any way to plot other branches of the Hypergeometric
> function in Mathematica.  I can plot the real component of the
> "principal" branch with this:
>
> F[z_] := Hypergeometric2F1[1/2 - I/2, 1, 3/2 - I/2, z]
> p1 = Plot3D[Evaluate[Re[F[z] /. z -> x + I*y]], {x, -5, 5},
>      {y, -5, 5}, Exclusions -> {y == 0}, PlotRange -> All]
>
> and integrating the Hypergeometric differential equation across the
> principal branch cut, I can "get at" other branches.
>
> Is there any nice way in Mathematica to plot the second branch?


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