Accurate Approximation of Factorial Size
Problem
The user wants a more precise estimation of factorial magnitude, especially in algorithm analysis and statistical mechanics. Current fast approximations like n·lg n are insufficient, and they need a tighter formula or tool.
Pain points
- Need a more accurate factorial approximation formula
- Dissatisfied with the error of existing approximations
- Desire a quick way to estimate the number of digits of a factorial
Questions to verify
- Do you frequently need to quickly estimate the number of digits or size of a factorial?
- Is your current approximation method meeting your precision requirements?
- Would you be willing to use a tool or API that provides precise factorial estimation?
Evidence
quote · @匿名
A quick and dirty approximation of the number of digits in n! is n lg n, which approximates n! from above, via the inequality
quote · @匿名
Stirling's approximation is also used a lot in statistical mechanics, because you often have to calculate logs of state space sizes, which means lots of combinatorics and thus lots of factorials.
quote · @匿名
lg(n!) grows roughly as (n lg n). Constants matter, of course, but to that's the rough estimate.
fact · @匿名
ln n! = n ln n - n + O(ln n).
Disclaimer: this card is distilled by AI from community discussions as “pain point evidence”. It is a starting point for need analysis and validation, not a “validated market need”. AI has analytical limits; please open the original discussion above to manually verify before key decisions.