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Quadratic transformation inequalities for Gaussian hypergeometric function
Tie-Hong Zhao1, Miao-Kun Wang2, Wen Zhang3
11Department of Mathematics, Hangzhou Normal University, Hangzhou, China.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study introduces quadratic transformation inequalities for the Gaussian hypergeometric function. It also establishes duplication inequality analogs for the generalized Grötzsch ring function.
Area of Science:
- Mathematics
- Special Functions
- Inequalities
Background:
- The Gaussian hypergeometric function is a fundamental object in mathematical analysis.
- Inequalities play a crucial role in understanding the behavior of special functions.
- The generalized Grötzsch ring function is relevant in geometric function theory.
Purpose of the Study:
- To derive novel quadratic transformation inequalities for the Gaussian hypergeometric function.
- To establish analogs of duplication inequalities for the generalized Grötzsch ring function.
Main Methods:
- Utilizing techniques from the theory of inequalities.
- Applying methods related to the analysis of special functions.
- Developing transformations for hypergeometric functions.
Main Results:
- Several new quadratic transformation inequalities for the Gaussian hypergeometric function have been established.
- The study successfully found analogs of duplication inequalities for the generalized Grötzsch ring function.
Conclusions:
- The findings contribute to the theory of inequalities for special functions.
- The results provide new tools for analyzing the generalized Grötzsch ring function.
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