Modification of the Stirling Formula
In mathematics, the Stirling formula (Mohawra-Stirling) is known - a formula for the approximate calculation of factorial and gamma functions [ Stirling formula ]:
The formula is good and gives a fairly accurate approximation for large values of n. For small values, the formula gives a significant error.
Empirically, I obtained an additional coefficient, which makes it possible to almost completely get rid of the error at small values of n:
Comparing the calculation results using the above formulas, we see that the modified version practically does not give an error:
PS And we call the resulting formula "Moavre-Stirling-Koshelenko formula" :)
The formula is good and gives a fairly accurate approximation for large values of n. For small values, the formula gives a significant error.
Empirically, I obtained an additional coefficient, which makes it possible to almost completely get rid of the error at small values of n:
Comparing the calculation results using the above formulas, we see that the modified version practically does not give an error:
PS And we call the resulting formula "Moavre-Stirling-Koshelenko formula" :)
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Source: https://habr.com/ru/post/109984/
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