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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).

Matthew Scott
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  • See https://math.stackexchange.com/questions/98481/is-a-factorial-an-algebraic-function-and-an-elementary-function – lhf Feb 19 '22 at 17:50
  • @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. – Snaw Feb 19 '22 at 18:02
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    I have found an answer here: https://math.stackexchange.com/questions/1343452/any-shortcut-to-calculate-factorial-of-a-number-without-calculator-or-n-to-1 – Matthew Scott Feb 19 '22 at 18:06
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    Also https://math.stackexchange.com/questions/1392728/proof-that-the-factorial-is-nonelementary – lhf Feb 19 '22 at 18:07
  • 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: https://www.maa.org/programs/maa-awards/writing-awards/the-factorial-function-and-generalizations ) –  Feb 19 '22 at 18:12

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