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2012 | 10 | 2 | 775-787
Tytuł artykułu

An asymptotic approximation of Wallis’ sequence

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Treść / Zawartość
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Języki publikacji
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} $ .
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
2
Strony
775-787
Opis fizyczny
Daty
wydano
2012-04-01
online
2012-01-18
Twórcy
autor
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0138-4
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