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    $\begingroup$ (+1) Great answer like this again! $\endgroup$ Commented Sep 23, 2024 at 3:42
  • $\begingroup$ @A.Kato thank you $\endgroup$ Commented Sep 23, 2024 at 5:28
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    $\begingroup$ Maybe a simpler path to the same result: replace the sum by an integral. Then justify that the difference is o(1) as r->infinity. (Roughly: denominator of each term ->0 while numerators change more slowly in r.) $\endgroup$ Commented Sep 23, 2024 at 16:40
  • $\begingroup$ @DanielLichtblau Ah yes, this does work! Especially if you IntegrateChangeVariables with t==Sqrt[-1+k] . I can add it to the answer if you want, but if you want to post it as your own answer that would be cool (since it was your idea). $\endgroup$ Commented Sep 23, 2024 at 17:05
  • $\begingroup$ I'll post it in a bit. Different methods can be useful to have in answers. $\endgroup$ Commented Sep 23, 2024 at 17:36