An approximation formula for n!

  • Necdet Batir Nevsehir Haci Bektas Veli Üniversitesi.
Palabras clave: Gamma function, Stirling formula, Euler-Mascheroni constant, Harmonic numbers, Inequalities, Digamma function.

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 9871η! 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 with32 32 ״ n 176 128, r- (η\n8/ΙΓ־Α 32176 ~־ η! Pá ץ/π — \ 16η4 + — η3 + — η2+ —— η Ve/ V 3 9 4053 9 405 1215which is established by C. Mortici in his very new paper [8].

Citas

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Cómo citar
Batir, N. (1). An approximation formula for n!. Proyecciones. Journal of Mathematics, 32(2), 173-181. https://doi.org/10.4067/S0716-09172013000200006
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