Abstract
Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s integral inequality. We also studied the monotonicity, log-concavity, and log-convexity of extended hypergeometric functions, which are derived by using the inequalities on an extended beta function.
Highlights
Introduction and PreliminariesIn mathematics, the theory of special functions is an area that plays a vital role due to its applications in real analysis, functional analysis, geometry, physics, and many more subjects of science
Inequalities and extensions are both important topics in the theory of special functions, but from a theoretical point of view, very few inequalities involving hypergeometric functions and extended hypergeometric functions seem to have appeared in the literature until now
We conclude our investigation by remarking that here, we describe some new inequalities including the extended type Gauss hypergeometric function and confluent hypergeometric function, respectively
Summary
Introduction and PreliminariesIn mathematics, the theory of special functions is an area that plays a vital role due to its applications in real analysis, functional analysis, geometry, physics, and many more subjects of science. Inequalities and extensions are both important topics in the theory of special functions, but from a theoretical point of view, very few inequalities involving hypergeometric functions and extended hypergeometric functions seem to have appeared in the literature until now. Goyal and Jain et al [9,10] have extended the beta function, Gauss hypergeometric function, confluent hypergeometric function and studied various properties of these extended functions. They studied the increasing or decreasing nature (monotonicity), log-concavity, and log-convexity of extended beta function in [10]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
