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  • $\begingroup$ It's a bit like what I did here, yes? :) Still, your solution can benefit greatly from using the Kummer-transformed version of the function. $\endgroup$ Commented Aug 4, 2012 at 10:17
  • $\begingroup$ @J.M. oops, I did not remember that! (I did remember seeing this somewhere but not where). I've added a link! About the transformation, I agree, but I try to avoid specializing things unless absolutely necessary and, in this case, it's not; so I left it general. Plus, it's well described in your post. $\endgroup$ Commented Aug 4, 2012 at 11:05
  • $\begingroup$ @J.M. as an aside, seeing that transformation reminds me of a few days of pain resulting from having to manipulate a complicated combination of 2F1 functions a few years ago. In the event, it took more computer time to explicitly evaluate the analytical solutions (which I obtained in the form of series) than to do numerical simulations of the system. That taught me a lesson! $\endgroup$ Commented Aug 4, 2012 at 11:08
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    $\begingroup$ Heh. Still, sometimes analytical manipulations can yield a form that is eminently more suitable for numerics, so it still pays to try out an identity or two... $\endgroup$ Commented Aug 4, 2012 at 11:12
  • $\begingroup$ @J.M. yes, that is pretty much the bulk of my working day, some days. $\endgroup$ Commented Aug 4, 2012 at 11:13