On the approximation of the Wallis ratio
Keywords:
approximation; double inequality; Wallis formula; Wallis ratio
Abstract
In this review article, we study the recent investigations and developments on the Wallis ratio. Some best constants for the approximation of the Wallis ratio are introduced. Some double inequalities for bounding the Wallis ratio are also introduced.
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References
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[9] S. Guo, J. Xu and F. Qi, Some exact constants for the approximation of the quantity in the Wallis’ formula, J. Inequal. Appl. 2013(2013), Article ID 67.
[10] S. Guo, Q. Feng, Y. Bi and Q. Luo, A sharp two-sided inequality for bounding the Wallis ratio, J. Inequal. Appl. , 2015(2015), Article ID 43.
[2] M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematics Series 55, Washington, 1970.
[3] D. S. Mitrinovi´c, Analytic Inequalities, Springer-verlag, Berlin, 1970.
[4] C. Chen and F. Qi, The best bounds in wallis’ inequality, Proc. Amer. Math. Soc., 133(2005), 397-401.
[5] Y. Zhao and Q.Wu,Wallis inequality with a parameter. J. Inequal. Pure Appl. Math. 7(2006), Article ID 56.
[6] C. Mortici, Completely monotone functions and the Wallis ratio. Appl. Math. Lett. 25(2012), 717–722.
[7] B. Guo and F. Qi, A class of completely monotonic functions involving divided differences of the psi and tri-gamma functions and some applications. J. Korean Math. Soc. 48(2011), 655–667.
[8] S. Guo and C. Song, A new result for the approximation of the quantity involved in the Wallis’ formula, Proceedings of the 2012 International Conference on Computer Science, Mathematics, Physical Education, and Management, Wuhan, China, September, 2012, IEEE
Press, pp. 259–262.
[9] S. Guo, J. Xu and F. Qi, Some exact constants for the approximation of the quantity in the Wallis’ formula, J. Inequal. Appl. 2013(2013), Article ID 67.
[10] S. Guo, Q. Feng, Y. Bi and Q. Luo, A sharp two-sided inequality for bounding the Wallis ratio, J. Inequal. Appl. , 2015(2015), Article ID 43.
Published
2019-01-11
How to Cite
Guo, S. (2019). On the approximation of the Wallis ratio. Journal of Progressive Research in Mathematics, 14(3), 2408-2412. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1677
Issue
Section
Review Article
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