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Refining trigonometric inequalities by using Padé approximant
Zhen Zhang1,2, Huaqing Shan2, Ligeng Chen2
11School of Cyberspace, Hangzhou Dianzi University, Hangzhou, China.
Journal of Inequalities and Applications
|July 17, 2018
Summary
A new two-point Padé approximant method refines trigonometric inequalities like Jordan
Area of Science:
- Mathematical Analysis
- Inequalities
- Approximation Theory
Background:
- Trigonometric inequalities are fundamental in mathematical analysis.
- Existing methods for refining these inequalities have limitations.
Purpose of the Study:
- To introduce and validate a novel two-point Padé approximant method.
- To refine key trigonometric inequalities: Jordan, Kober, Becker-Stark, and Wu-Srivastava.
Main Methods:
- Application of a two-point Padé approximant.
- Development of simplified proof techniques.
Main Results:
- The proposed method refines the specified trigonometric inequalities.
- Achieves superior approximation results compared to existing methods.
Conclusions:
- The two-point Padé approximant offers an effective approach for refining trigonometric inequalities.
- This method provides better accuracy and simpler proofs.
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