Modification of the Stirling formula
In mathematics, the Stirling formula (Moavre-Stirling) is known - the formula for the approximate calculation of the factorial and gamma function [ 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 have obtained an additional coefficient that allows us to almost completely get rid of the error for small values of n:
Comparing the results of the calculation using the above formulas, we see that the modified version practically does not give an error:
PS And we call the resulting formula the “Moirre-Stirling-Koshelenko Formula ":)
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 have obtained an additional coefficient that allows us to almost completely get rid of the error for small values of n:
Comparing the results of the calculation using the above formulas, we see that the modified version practically does not give an error:
PS And we call the resulting formula the “Moirre-Stirling-Koshelenko Formula ":)