In the MO-question on a lacunary series I wrote an answer (really: a comment) having the hypothese about an interesting fact (the function $d(x)$ as difference between the OP's function $f(x)$ and some modification $g(x)$ has constant amplitude). I could not provide more details for that heuristic.

I've now a further hypothese, which describes a power series solution for $d(x)$ which seems to work perfectly, but again besides the heuristical finding have no proof so far; while I've developed that hypothese in a fairly often applied framework of alternating series, a formal explanation for the correctness of the "mechanic" behind is out of reach for me.

SO is it better to present that power series -hypothese for $d(x)$ as a new question for help for a formal proof, or is it better just to include that hypothese into my previous answer/comment?


1 Answer 1


Given that your first answer is already pretty long and full of (nice-looking, but numerous) diagrams, I would personnally prefer a new question with link to the original problem.

  • $\begingroup$ I've now followed your proposal, thanks, and formulated some questions for the explanation/proofs of the heuristics, mathoverflow.net/questions/201098 It became so long again that indeed it likely were an overkill to add this to the old answer, and the open hypotheses require an official "question" anyway. I hope it also still fits our MO-rules... $\endgroup$ Mar 26, 2015 at 4:35
  • $\begingroup$ @GottfriedHelms : "I hope it also still fits our MO-rules... " -> There's no reason whatsoever to believe the opposite, imho. Even more since you like to develop and motivate your ideas, I'd personnally rather see this than a pair of lines ending with "help me please !!1!1!". $\endgroup$
    – Hachino
    Mar 26, 2015 at 7:49

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