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Re: Demonstrate that 1==-1
*To*: mathgroup at smc.vnet.net
*Subject*: [mg23220] Re: [mg23171] Demonstrate that 1==-1
*From*: "Kevin J. McCann" <kevinmccann at home.com>
*Date*: Tue, 25 Apr 2000 01:40:26 -0400 (EDT)
*References*: <8e0mhl$f25@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
f1[a_] := Integrate[ (-1 - a/E^(I*u))/(1 - a/E^(I*u)), {u, 0, 2*Pi}]
f2[a_] := Integrate[(1 + a/E^(I*u))/(-1 + a/E^(I*u)), {u, 0, 2*Pi}]
{f1[a],f2[a]} = {2*Pi, -2*Pi}
{f1[2],f2[2]} = {2*Pi, 2*Pi}
{f1[-2],f2[-2]} = {2*Pi, 2*Pi}
{f1[1/2],f2[1/2]} = {-2*Pi, -2*Pi}
Seems that it works fine with a definite choice for a, but not when a is a
variable. Not sure what Mathematica is assuming for a, or why. Ordinarily Mathematica puts
out a conditional answer where appropriate. Not so here for a > 1 or a < 1.
Normal behavior is that Mathematica puts out a conditional, not so here. This is a
BUG.
Cheers,
Kevin
"David Withoff" <withoff at wolfram.com> wrote in message
news:8e0mhl$f25 at smc.vnet.net...
> > Compute
> > Integrate[(1 + a/E^(I*u))/(-1 + a/E^(I*u)), {u, 0, 2*Pi}]
> >
> > Mathematica gives -2Pi
> >
> > Now multiply the numerator and the denominator by -1
> >
> > Integrate[(-1 - a/E^(I*u))/(1 - a/E^(I*u)), {u, 0, 2*Pi}]
> >
> > Mathematica gets 2*Pi
> >
> > This is only possible if 1==-1
>
> It is also possible if the first integral implicitly makes
> the assumption Abs[a]<1 and the second integral implicitly
> makes the assumption Abs[a]>1. Implicit assumptions like
> this are quite common in definite Integrate with symbolic
> parameters. Although it is often desirable for Integrate
> to report such assumptions, that does not yet happen in
> all examples.
>
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