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I have discovered a new formula that approximates the factorial function. It is more accurate than Stirling’s approximation. How do I go about publishing it and receive the credit for it?

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    $\begingroup$ What is your definition of $x!$? $\endgroup$ – uniquesolution Jul 16 at 7:17
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    $\begingroup$ Please, let us know when you will publish it. It is a so important topic for all of us ! Thanks, cheers and good luck. $\endgroup$ – Claude Leibovici Jul 16 at 7:31
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    $\begingroup$ Note: math.stackexchange.com/questions/152342/… $\endgroup$ – Klangen Jul 16 at 8:29
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    $\begingroup$ Remember that, despite the wider use of Stirling's one, there exist other formulas for approximating the factorial $n!$ to higher precision (see also @Klangen's comment): for example, Francesco Tricomi mentions one of them in a didactic paper on the Landau symbols $o$ and $O$. If you can, review the literature by using Zentralblatt and the Mathematical Reviews in order to see if it has already been published or nevertheless look for other formulas in order to make a nice historical introduction to your paper. $\endgroup$ – Daniele Tampieri Jul 16 at 9:22
  • $\begingroup$ You may also look in this paper of G. Nemes (10.1007/s00013-010-0146-9) with $(x-1)!=\Gamma(x)\approx (\frac{x}{e})^x\sqrt{2\pi/x}(1+\frac{1}{12x^2-1/10})^x$ $\endgroup$ – yarchik Jul 16 at 10:45
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Well, you could first publish it at https://arxiv.org/, section Mathematics. Then you could go for a combinatorics journal. However, stay away from the predatory journals, here is a list of them: https://beallslist.weebly.com/. All journals not on this list can be viewed as non-predatory journals. Pick one of them. Journals are ranked by ''impact factor''. Pick a journal with a higher impact factor such as in https://www.scimagojr.com/journalrank.php. This will give you more credit, a higher reputation. After picking a journal, follow the author guidelines on the journal's homepage to submit the manuscript (usually PDF). Good luck!

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  • $\begingroup$ There exist non-predatory journals? $\endgroup$ – mathreadler Jul 16 at 7:30
  • $\begingroup$ See added comment. $\endgroup$ – Wuestenfux Jul 16 at 7:37
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    $\begingroup$ yeah yeah I know what you mean, I was just being sarcastic $\endgroup$ – mathreadler Jul 16 at 8:16
  • $\begingroup$ Thank you the feed back and honesty. Much appreciated. $\endgroup$ – Rob Jul 16 at 14:57

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