Estimates for Wallis’ ratio and related functions

Cristinel Mortici () and Valentin Gabriel Cristea ()
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Cristinel Mortici: Valahia University of Târgovişte
Valentin Gabriel Cristea: University Politehnica of Bucharest

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 437-447

Abstract: Abstract We present improvements of approximation formula for Wallis ratio related to a class of inequalities stated in [D.-J. Zhao, On a two-sided inequality involving Wallis’s formula, Math. Practice Theory, 34 (2004), 166-168], [Y. Zhao and Q. Wu, Wallis inequality with a parameter, J. Inequal. Pure Appl. Math., 7(2) (2006), Art. 56] and [C. Mortici, Completely monotone functions and the Wallis ratio, Applied Mathematics Letters, 25 (2012), 717-722]. Some sharp inequalities are obtained as a result of monotonicity of some functions involving gamma function.

Keywords: Wallis ratio; Gamma function; polygamma function; complete monotonicity; speed of convergence; inequalities (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0176-5

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