2018/02/20 by Nader H. Bshouty, Bshouty, Nader H., Vivian E. Bshouty-Hurani +9
Mathematics · #Advanced Mathematical Identities #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications
paper · pdf · doi:10.48550/arxiv.1802.07046
openalex publication_date 2018/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give elementary proofs of several Stirling's precise bounds. We first improve all the precise bounds from the literature and give new precise bounds. In particular, we show that for all n≥ 8 √(2πn)((n)/(e))n e(1)/(12n)-(1)/(360n3+103n) ≥ n!≥ √(2πn)((n)/(e))n e(1)/(12n)-(1)/(360n3+102n) and for all n≥ 3 √(2πn)((n)/(e))n e(1)/(12n+(2)/(5n)-(1.1)/(10n3)) ≥ n!≥ √(2πn)((n)/(e))n e(1)/(12n+(2)/(5n)-(0.9)/(10n3)).