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• # Artykuł - szczegóły

## Open Mathematics

2012 | 10 | 2 | 775-787

## An asymptotic approximation of Wallis’ sequence

EN

### Abstrakty

EN
An asymptotic approximation of Wallis’ sequence W(n) = Πk=1n 4k 2/(4k 2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates of Wallis’ ratios w(n) = Πk=1n(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example, $W(n) \cdot (a_n + b_n ) < \pi < W(n) \cdot (a_n + b'_n )$ with $a_n = 2 + \frac{1} {{2n + 1}} + \frac{2} {{3(2n + 1)^2 }} - \frac{1} {{3n(2n + 1)'}}b_n = \frac{2} {{33(n + 1)^{2'} }}b'_n \frac{1} {{13n^{2'} }}n \in \mathbb{N}$ .

EN

775-787

wydano
2012-04-01
online
2012-01-18

### Twórcy

autor
• University of Ljubljana

### Bibliografia

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