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    $\begingroup$ What do you mean by "substituting the denominator with an integral"? I mean, you can do Integrate @@ Sum[ ... ], but that probably won't be equal to the original expression and in any event Mathematica doesn't evaluate that either. $\endgroup$ Commented May 31, 2016 at 19:25
  • $\begingroup$ I added the brief explanation in the upd. $\endgroup$ Commented Jun 1, 2016 at 11:27
  • $\begingroup$ @HaykHakobyan your link of $a_0$ may be broken. Please check it. $\endgroup$ Commented Oct 10, 2017 at 10:57
  • $\begingroup$ @tanghe2014 fixed, thnx. $\endgroup$ Commented Oct 10, 2017 at 21:28