An approximation formula for n!

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  1. [1] Nevşehir Hacı Bektaş Veli University

     Nevşehir Hacı Bektaş Veli University

     Turquía

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 32, Nº. 2, 2013, págs. 173-181
• Idioma: inglés
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• 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\n 8/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].