Skip to main content
Mathematica

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

12
  • $\begingroup$ Just a sanity check: Do you have any reason to believe that the integral were finite? $\endgroup$ Commented Apr 3, 2020 at 17:53
  • $\begingroup$ @HenrikSchumacher Yes, the integral diverges at $\epsilon = 0$ but is finite for other positive values of $\epsilon$ (note the integration limits for $x$). I have already performed a set of such measurements overnight at low accuracy which confirmed that. Why would you think it is not finite? $-0.180996$ is not a high number. $\endgroup$ Commented Apr 3, 2020 at 17:57
  • $\begingroup$ Related to my previous comment: the integrand takes its highest values for $x$ near $1-\epsilon/2$, maybe that is a useful information. $\endgroup$ Commented Apr 3, 2020 at 18:06
  • 1
    $\begingroup$ It is not much, but the can reduce this by one dimensions by using polar coordinates for {u,z}: y and z appear always together as y^2 + z^2. $\endgroup$ Commented Apr 6, 2020 at 6:50
  • 1
    $\begingroup$ Just a side note: Do not forget to multply the integrand by 2 Pi r before integrating over r to account for the change in coordinates. $\endgroup$ Commented Apr 6, 2020 at 9:25