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A Simple Asymptotic Estimate of Wallis’ Ratio Using Stirling’s Factorial Formula

  • Vito Lampret
Article

Abstract

Several new, accurate, simple, asymptotic estimates of Wallis’ ratio \(w_n:=\prod \nolimits _{k=1}^{n} \frac{2k-1}{2k}\) are obtained on the bare the Bernoulli coefasis of Stirling’s factorial approximation formula. Some asymptotic estimates of \(\pi \) in terms of Wallis’ ratios \(w_n\) are also presented.

Keywords

Approximation Estimate Inequality \(\pi \) Rate of convergence Wallis’ ratio 

Mathematics Subject Classification

26D20 41A60 65B99 (11Y99) 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.University of LjubljanaLjubljanaSlovenia

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