I recently posted this question with an answer to it as well. I got two immediate downvotes, I'm not quite sure what I did wrong as it was a feature in stack exchange to be able to answer one's own question.

The idea behind me posting that question was that, this was something I had been searching for long and I found a nice non-induction proof, so I posted but immediately people are saying this won't help anyone. I'm quite confused on that because if someone who is interested in how to do in this method, then he would find it?

So, I wish to know what is the general stance of the community. Thank you.

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    $\begingroup$ Note for future readers here: it seems in this case you did not actually need feedback about your solution, but your goal was rather "sharing." I think in general we've not encouraged this because if condoned it could be used to justify mass-producing poor content. We prefer to prioritize people with questions they actually face. Proactively posting problem-solution pairs hoping other people will find and read them is not a bad idea in principle, but the problem is that it will usually not be searched for. Better the person with the problem actually asks for themself. $\endgroup$ – rschwieb Sep 2 '20 at 20:15
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    $\begingroup$ Is upvoting this question agreement that it is frowned upon? Or is that the case for downvoting it? (Also, what was the reason for the questions closure? Was it lacking motivation? Did it lack context? It clearly had a good title, correct tags, Mathjax, good formatting, and wasn't a 'no clue' question.) $\endgroup$ – user400188 Sep 3 '20 at 0:26
  • $\begingroup$ For this particular Q&A, in terms of site organization it would better to find a (the?) general question on how to prove the Leibniz product rule, and add your answer as an answer there. Start your answer with "here's an approach that doesn't use induction." Like, your answer might be new and interesting, but I don't think your question is new. $\endgroup$ – Mike Pierce Sep 10 '20 at 23:02

Self-answered questions are allowed, even encouraged on Stack Exchange.

Stack Exchange has always explicitly encouraged users to answer their own questions. If you have a question that you already know the answer to, and you would like to document that knowledge in public so that others (including yourself) can find it later, it's perfectly okay to ask and answer your own question on a Stack Exchange site.

However, self-answered questions are still subject to the same quality rules as others. The question you linked to looks like a PSQ to me, and those questions are often (rightfully) down- and close-voted. In practice, they're often held to higher quality standards by the community, which might explain the downvote on the answer.

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    $\begingroup$ I'd daresay that self-answered questions are not subject to the same quality rules, but to higher ones. If you are writing the question and the answer, then you have all the time in the world to do the work properly and to submit nothing less than a great question and a great answer. This, at the very least, is necessary to dispel any concerns of just chasing reputation. $\endgroup$ – Asaf Karagila Sep 2 '20 at 11:38
  • $\begingroup$ That's mentioned in the second part of the paragraph. It's not mentioned in the 'rules', but it is what happens in practice. $\endgroup$ – Glorfindel Sep 2 '20 at 11:45
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    $\begingroup$ @Asaf this seems odd to me. We don't like the PSQ, in part because they show no effort on the part of the user asking, in part because we worry someone is trying to get us to do his homework for him. But if the person posting the question is also posting an answer, those objections to the PSQ don't apply. $\endgroup$ – Gerry Myerson Sep 2 '20 at 11:57
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    $\begingroup$ @Gerry: No, that's a symptom, but we don't like PSQs because they are not good questions in most cases. I can think of several PSQs that are actually decent questions, usually because those are questions so advanced that the context is implicitly clear to anyone who understands the question. $\endgroup$ – Asaf Karagila Sep 2 '20 at 11:58
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    $\begingroup$ I think the notion of a "self-answered PSQ" is an oxymoron. In the past we've discussed how the proffered solution counts towards context. I think the more important barometer is how the user is employing this ability: are they seeking critical feedback on something they're not completely sure is correct, or are they mass-producing stuff for the sake of producing? $\endgroup$ – rschwieb Sep 2 '20 at 20:08
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    $\begingroup$ @rschwieb Seeking critical feedback and mass producing stuff are not the only possible cases. A user could be writing the self answer question simply to improve their ability to convey a proof on a topic they are interested in (rather than one set by another asker) to a larger audience than normal. $\endgroup$ – user400188 Sep 3 '20 at 0:24
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    $\begingroup$ @user400188 Sure, I never intended it to be comprehensive, only suggestive of good and bad aspects. That’s an ok use too. $\endgroup$ – rschwieb Sep 3 '20 at 1:16
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    $\begingroup$ My view is that self-answering should be held to higher standards. In particular PSQs should be avoided. Adding motivation, a bit of history/source of problem and the thought process behind finding a solution helps to make the question damn interesting. In a few cases some of my questions were not intended to be self answered but later I figured a solution and posted it. $\endgroup$ – Paramanand Singh Sep 3 '20 at 7:17
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    $\begingroup$ @AsafKaragila: I have mixed feelings about advanced level PSQs. I feel that we can add some minimal context to make it a bit less advanced and accessible to a wider audience. However I do agree that we don't need to close them for lack of context. $\endgroup$ – Paramanand Singh Sep 3 '20 at 7:21
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    $\begingroup$ Downvote due to poor quality might be one reason, but in this case it might caused by people simply not knowing that self-answering is recommended by the site (it's not that common after all), they see it as something strange ... $\endgroup$ – Sil Sep 3 '20 at 19:10
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    $\begingroup$ I am willing to upvote self-answered questions in which the question seems sincerely to be a question, and context, not necessarily effort is shown, and the the asker then gains insight, from comments, hints, or more time thinking about the question, and returns to answer. I am not at all fond of staged Q&A's in which the asker asks a PSQ, already knowing the answer (in which case, there really is no honest question being asked), and almost immediately proceeds to answer their pseudo-question. $\endgroup$ – amWhy Sep 3 '20 at 22:16
  • $\begingroup$ This OP's question seems clearly to be in the latter camp. $\endgroup$ – amWhy Sep 3 '20 at 22:17

I agree with this comment on the question: "[...] For self answering do try to start with a question which is not already available on mathse and add good amount of context." − Paramanand Singh

The point is that Math SE is not supposed to be a blog for anyone to just post whatever they like. If you have some question that you know the answer to, and the question has not been asked before, and your answer does not seem to be available anywhere on Math SE, and you have expertise in that topic, then it makes sense to post a Q&A pair. If the answer has been posted before, it clearly should not be posted again. If the question has been asked before, you ought to post your answer there instead of contributing to the question duplicates on Math SE. If you are not sure that your answer is of high quality, then you should put it in your question and ask for feedback rather than putting it forth as a model answer.

In particular, a one-minute search yields this old Math SE thread which in my opinion also has far better answers than yours. Firstly, because (as pointed out by Arctic Char) your proof only works in the limited case that the two given functions are analytic, which is not only completely unnecessary but also mathematically irrelevant to the true essence of the theorem. Secondly, because the proof in the older thread very intuitively and clearly shows why the theorem is true, so much so that it is obvious to everyone that the usual combinatorial proof of the usual binomial theorem for natural exponents can be translated into a proof of the desired theorem.

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    $\begingroup$ I agree with this. On StackOverflow the idea is that anyone working with some system might come across a problem, find a solution, and that solution is likely to be useful to others coming across the same problem. In mathematics, that is hardly ever the case, so unless you have some actual expertise in the specific topic, your question/answer pair is unlikely to be of much interest. $\endgroup$ – Tobias Kildetoft Sep 13 '20 at 12:51
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    $\begingroup$ @TobiasKildetoft: Incidentally, totally unrelated to this thread but related to your comment, there are other users who deliberately post Q&A pairs to promote their crankery. It is amusing to note that crankery does not seem to show up on SO simply because there is nothing to gain from posting nonsense, but it shows up on SE sites where readers may not have the expertise to evaluate answers for their correctness or usefulness. $\endgroup$ – user21820 Sep 13 '20 at 12:57
  • $\begingroup$ You're correct. I did not of the thread before, I searched it but I couldn't find it. What do you suggest I do? $\endgroup$ – Buraian Sep 13 '20 at 13:58
  • $\begingroup$ @Buraian: Thanks for responding! Personally, I suggest you delete the thread, primarily because of the two reasons I gave in my last paragraph, and not just because it was a duplicate. In the future, I suggest that you ask for feedback by putting your proof attempt in your question, and you can be sure that nobody will criticize you for that. =) $\endgroup$ – user21820 Sep 13 '20 at 14:01
  • $\begingroup$ As for finding the question in an existing thread, I simply used the Math SE search and it was right there on the first page of results. $\endgroup$ – user21820 Sep 13 '20 at 14:03
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    $\begingroup$ I might have missed it, decided to accept duplicate as the method in that linked post was different from mine, and, I'd also like to note that the user who answered in that post with Taylor method also took assumptions on the function. As a personal note, I felt your answer was unnecessarily attacking at certain instances once I read the other answer, and, I did not really appreciate how I was grouped with 'cranks'. Maybe these were not your intentions but it is rude to be like that. $\endgroup$ – Buraian Sep 13 '20 at 14:08
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    $\begingroup$ @Buraian: I purposely stated that the crankery I mentioned to Tobias was totally unrelated to this thread. I merely stated that to Tobias because he mentioned a difference between SO and Math SE. Not related to you at all. So I was not rude at all. Please read what I write more carefully, thanks. $\endgroup$ – user21820 Sep 13 '20 at 15:33

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