scholarly journals New Refinements and Improvements of Some Trigonometric Inequalities Based on Padé Approximant

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lina Zhang ◽  
Xuesi Ma
Keyword(s):  
Padé Approximant ◽  
Multiple Point ◽  
Trigonometric Functions ◽  
Pade Approximant ◽  
Trigonometric Inequalities ◽  
Jordan’S Inequality ◽  
Better Than ◽  
Approximant Method

A multiple-point Padé approximant method is presented for approximating and bounding some trigonometric functions in this paper. We give new refinements and improvements of some trigonometric inequalities including Jordan’s inequality, Kober’s inequality, and Becker-Stark’s inequality. The analysis results show that our conclusions are better than the previous conclusions.

The rise of a cylindrical bubble in an inviscid liquid

1982 ◽  
Vol 60 (7) ◽  
pp. 999-1007 ◽  
Author(s):  
R. T. Baumel ◽  
S. K. Burley ◽  
D. F. Freeman ◽  
J. L. Gammel ◽  
J. Nuttall
Keyword(s):  
Gravitational Field ◽  
Padé Approximant ◽  
Inviscid Liquid ◽  
Pade Approximant ◽  
Approximant Method

An expansion in powers of t2 is obtained which gives the shape of an initially horizontal cylindrical bubble filled with a massless gas as it rises through an incompressible inviscid infinite fluid in a uniform vertical gravitational field. For larger times the series does not converge but we have found that a variation of the Padé approximant method gives good results for the locations of the top and bottom of the bubble, although not for times quite as large as might be desired. The results compare favourably with experiment.

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