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Monotonicity properties and bounds for the complete p-elliptic integrals
Ti-Ren Huang1, Shen-Yang Tan2, Xiao-Yan Ma1
11Department of Mathematics, Zhejiang Sci-Tech Universityu, Hangzhou, China.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study extends monotonicity and convexity properties, along with sharp inequalities, from complete elliptic integrals to complete p-elliptic integrals, advancing mathematical analysis.
Area of Science:
- Mathematical Analysis
- Special Functions
Background:
- Complete elliptic integrals are fundamental in mathematical physics and analysis.
- Generalizing their properties to p-elliptic integrals remains an active area of research.
Purpose of the Study:
- To generalize monotonicity and convexity properties of complete elliptic integrals.
- To establish sharp inequalities for complete p-elliptic integrals.
Main Methods:
- Leveraging existing theories of elliptic integrals.
- Applying generalization techniques to p-elliptic integral definitions.
Main Results:
- Successfully generalized key monotonicity properties.
- Extended convexity properties to the p-elliptic integral context.
- Derived sharp inequalities for complete p-elliptic integrals.
Conclusions:
- The study provides a unified framework for understanding p-elliptic integrals.
- These findings contribute to the theory of special functions and their applications.
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