Matthew Dodelson
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 Jan14 accepted Asymptotic behavior of an integral Jan13 comment Asymptotic behavior of an integral Sure, but it makes the $\epsilon$ divergence worse, because this comes from small $x$. Jan13 answered Asymptotic behavior of an integral Jan13 comment Asymptotic behavior of an integral @Zarrax, I tried this, but doesn't differentiating the denominator actually make the divergence worse instead of better? Am I missing something? Jan13 comment Asymptotic behavior of an integral As a simple counterexample, take the integral $\int dx_1\, dx_2\, e^{-x_1-x_2}/(x_1+x_2)^2$, where the range is from $\epsilon$ to $\infty$. We can make the orthogonal change of variables $y_1=x_1+x_2$ and $y_2=x_1-x_2$, and the integral now becomes $\int dy_1\, dy_2\, e^{-y_1}/y_1^2$, which would seem to diverge by your argument. This integral is explicitly convergent though, so $y_2$ must enter through the bounds. Jan13 comment Asymptotic behavior of an integral Hmmm I don't think so... $y_4$ still enters through the bounds on the other integrals, so I don't think it diverges. Jan12 comment Asymptotic behavior of an integral This method looks like it will work. I'll give it a shot and accept this answer if it does. Jan12 comment Asymptotic behavior of an integral @IgorRivin, in your improved answer I still get a Jacobian with zero determinant. However $x_4=y_4$ seems to work. Jan12 awarded Critic Jan12 awarded Supporter Jan12 comment Asymptotic behavior of an integral I haven't tried that yet, I'll look into that. Thanks. Jan12 comment Asymptotic behavior of an integral I tried that, but unfortunately the Jacobian determinant is zero for that transformation. Jan12 comment Asymptotic behavior of an integral Thanks for the tip, I simplified this. Jan12 asked Asymptotic behavior of an integral Oct3 awarded Scholar Oct3 accepted Lax Pairs for Linear PDEs Jan9 awarded Student Jan9 asked Lax Pairs for Linear PDEs