Padé approximants for inverse trigonometric functions and their applications
1Department of Mathematics, Longyan University, Longyan, Fujian 364012 P.R. China.
Journal of Inequalities and Applications
|February 21, 2017
Summary
This study refines inequalities for inverse trigonometric functions using the Padé approximation method. The new inequalities offer greater accuracy than previously established ones.
Area of Science:
- Mathematical Analysis
- Approximation Theory
Background:
- Inequalities are fundamental in various mathematical fields.
- Inverse trigonometric functions have diverse applications.
- Existing inequalities may lack sufficient precision for certain applications.
Purpose of the Study:
- To refine existing inequalities involving inverse trigonometric functions.
- To introduce novel inequalities with enhanced accuracy.
- To demonstrate the efficacy of the Padé approximant in inequality refinement.
Main Methods:
- Application of the Padé approximant technique.
- Derivation of new inequalities for inverse trigonometric functions.
- Comparative analysis of the refined inequalities against existing ones.
Main Results:
- Successfully generated refined inequalities for inverse trigonometric functions.
- The new inequalities provide a tighter bound compared to prior results.
- Demonstrated the superiority of the Padé approximant in this context.
Conclusions:
- The Padé approximant is a powerful tool for improving mathematical inequalities.
- The newly derived inequalities offer significant advancements in precision.
- This work contributes to the ongoing development of analytical inequalities.
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