Inequalities and asymptotic expansions of the Wallis sequence and the sum of the Wallis ratio (Q2879466)
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scientific article; zbMATH DE number 6338668
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities and asymptotic expansions of the Wallis sequence and the sum of the Wallis ratio |
scientific article; zbMATH DE number 6338668 |
Statements
Inequalities and asymptotic expansions of the Wallis sequence and the sum of the Wallis ratio (English)
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2 September 2014
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Wallis sequence
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gamma function
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identities
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inequality
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asymptotic expansion
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Bernoulli's numbers
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Bernoulli's polynomials
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Euler's numbers
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The authors present some asymptotic formulas for the Wallis sequence. Also some formulas as continued fractions are proven. The asymptotic formulas are obtained starting form the classical asymptotic series of the gamma function and of the ratio of gamma function. These formulas are truncated to obtain new accurate estimates for the Wallis ratio. The inequalities are stated using the Brouncker's continued fraction inequalities.
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