An approximation formula for n!
DOI:
https://doi.org/10.4067/S0716-09172013000200006Keywords:
Gamma function, Stirling formula, Euler-Mascheroni constant, Harmonic numbers, Inequalities, Digamma function.Abstract
We prove the following very accurate approximation formula for the factorial function:n!p ???-???(? + 1+ 72(3(¾¾¾!+!)2332800 -(^ +1? This gives better results than the following approximation formula
, at- n -n I 1 1 31 139 9871
?! Pá V27rnne n\ n +---1--------H---,
V 6 72n 6480n2 155520?3 6531840?4'
which is established by the author [5] and C. Mortici [16] independently, and gives similar results with
32 32 ? n 176 128
, r- (?\n8/???? 32176 ~? ?! Pá ?/? — \ 16?4 + — ?3 + — ?2+ —— ? Ve/ V 3 9 405
3 9 405 1215
which is established by C. Mortici in his very new paper [8].
References
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