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Re: Weirdness from double integrals?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95755] Re: Weirdness from double integrals?
  • From: Erik Max Francis <max at alcyone.com>
  • Date: Mon, 26 Jan 2009 05:02:56 -0500 (EST)
  • References: <200901251153.GAA00724@smc.vnet.net> <glj8e1$doa$1@smc.vnet.net>

danl at wolfram.com wrote:

> There are many subtleties to this. First, if you do an explicit multiple
> integral (that is, using ont Integrate rather than iterating several of
> them), then the GenerateConditions option is only used for the last
> integration. This is documented but certainly constitutes "fine print".
> For the GenerateConditions->False behavior of prior integrals, it is
> common that they might give a spurious zero due to splitting ranges and
> making conflicting hidden assumptions on parameters that cause results to
> be not everywhere applicable.
> 
> One possible way around might be to set GenerateConditions->True so that
> it will be in effect for all levels of the integration.
> 
> Integrate[integrand[[3]], {x, -x0, x0}, {y, -y0, y0},
>  GenerateConditions -> True]
> 
> Problem now is Mathematica 7 claims this diverges. I need to look into
> this more closely, but offhand I have to say this looks like a bug in
> convergence testing.

Okay, so there _is_ something goofy going on here.

> As you have found, best is to give applicable assumptions. This variant
> gives a useful result.

I've verified this works.  Thanks.

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