An approximation formula for n!

NECTED BATIR

Resumen


We prove the following very accurate approximation formula for the factorial function:

n!p ηηε-ηφπ(η + 1+ 72(3(¾¾¾!+!)2332800 -(^ +1״ This gives better results than the following approximation formula

, at- n -n I 1 1 31 139 9871

η! Pá V27rnne n\ n +---1--------H---,

V 6 72n 6480n2 155520η3 6531840η4'

which is established by the author [5] and C. Mortici [16] independently, and gives similar results with

32 32 ״ n 176 128

, r- (η\n8/ΙΓ־Α 32176 ~־ η! Pá ץ/π — \ 16η4 + — η3 + — η2+ —— η Ve/ V 3 9 405

3 9 405 1215

which is established by C. Mortici in his very new paper [8].


Palabras clave


Gamma function ; Stirling formula ; Euler-Mascheroni constant ; Harmonic numbers ; Inequalities ; Digamma function.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172013000200006

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