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I am aware that there is a formula to calculate the sum of an arithmetic series. Is there a formula to calculate a product of an arithmetic series... in particular a factorial.

I am aware of the recursive / iterative algorithm which compute in linear time O(n) but I was wondering whether there is a formular so it can be computed in constant time O(1).

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  • $\begingroup$ See math.stackexchange.com/questions/98481/… $\endgroup$
    – lhf
    Commented Feb 19, 2022 at 17:50
  • $\begingroup$ @lhf That does seem like a duplicate, but unfortunately the only answer there is a low quality post about $n!$ not being a polynomial and contains a broken link to an article without as much as specifying its title, so it is not much help. $\endgroup$
    – Snaw
    Commented Feb 19, 2022 at 18:02
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    $\begingroup$ I have found an answer here: math.stackexchange.com/questions/1343452/… $\endgroup$
    – Matthew Scott
    Commented Feb 19, 2022 at 18:06
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    $\begingroup$ Also math.stackexchange.com/questions/1392728/… $\endgroup$
    – lhf
    Commented Feb 19, 2022 at 18:07
  • $\begingroup$ The Bhargava article referenced in the broken link may be this: "The Factorial Function and Generalizations", The American Mathematical Monthly, Vol. 107, 2000, pp.783-799. (At the risk of introducing another link that will be broken in the future, you can currently read it at the MAA link here: maa.org/programs/maa-awards/writing-awards/… ) $\endgroup$
    – user882145
    Commented Feb 19, 2022 at 18:12

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