Some Quicker Approximations and Inequalities of the Wallis Ratio by Continued Fraction

Liu, Xinyu; Lu, Dawei; Song, Lixin

doi:10.1007/s00025-015-0509-4

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Theorem 21 For Every S T ∈ R the Ratio Of The Gamma Func1

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2020

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“…In recent years, some authors paid attention to obtain better increasing approximations for the ratio of the gamma function in the form of continued fractions. For Liu et al (2015) has the approximation formula…”

Section: Theorem 21 For Every S T ∈ R the Ratio Of The Gamma Funcmentioning

confidence: 99%

Approximations for the Ratio of the Gamma Functions via the Digamma Function and Its Applications

Han

Zhang

You

et al. 2020

Bull Braz Math Soc, New Series

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In this paper, the authors establish some asymptotic formulas and two-sided inequalities for the ratio of the gamma function in terms of the digamma function. Considering the application of the gamma function to central Bernoulli coefficients, the authors give some better approximations and two-sided inequalities of central Bernoulli coefficients. Finally, for demonstrating the superiority of our results, some numerical computations are given. Keywords Digamma function • Ratio of the gamma function • Approximation • Power series expansion • Continued fraction • Central Bernoulli coefficients • Two-sided inequalities Mathematics Subject Classification 33B15 • 26D15 • 41A25

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Section: Theorem 21 For Every S T ∈ R the Ratio Of The Gamma Funcmentioning

confidence: 99%