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Manjul Bhargava had generalized the factorial function in number-theoretic context in this paper. At the end of the paper, he mentions some interesting problems associated with the generalized factorials.

I am particularly interested in the analogues of the Stirling's formula, Binomial coefficients and exponential function. So I want to know whether these problems are still unresolved and if so, then what is the present status of the research regarding these problems.

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    $\begingroup$ I recommend that you email the author of the paper about the future direction you are interested in. Ask for potential references. Do not expect the author to be as motivated as you are. Also keep the email short because do not expect the author to have a high time-commitment as you seem to have in approaching your questions. $\endgroup$ – Alberto Takase Feb 21 at 5:59
  • $\begingroup$ In other words, you are interested in the questions $31,32,33$? I think you should start with only one question here. First do a search yourself, so that you can ask a more specific question. $\endgroup$ – Dietrich Burde Feb 21 at 13:05

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