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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 summary is machine-generated.

This study introduces quadratic transformation inequalities for the Gaussian hypergeometric function. It also establishes duplication inequality analogs for the generalized Grötzsch ring function.

Keywords:

Duplication inequality Generalized Grötzsch ring function Hypergeometric function Quadratic transformation

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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.