A direct approach for proving Wallis ratio estimates and an improvement of Zhang-Xu-Situ inequality
Keywords:
Gamma function, Wallis ratio, asymptotic series, inequalities.Abstract
In time, inequalities about Wallis ratio and related functions were presented by many mathematicians. In this paper, we show how estimates on the Wallis ratio can be obtained using the asymptotic series. Finally, an improvement of an inequality due to X.-M. Zhang, T.-Q. Xu and L.-B. Situ [Geometric convexity of a function involving gamma function and application to inequality theory, J. Inequal. Pure Appl. Math. 8 (1) (2007) Art. 17, 9 pp.] is presented.
Mathematics Subject Classification (2010): 33B15, 34E05, 41A60.
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