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 ":)

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