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Some Inequalities of Extended Hypergeometric Functions

Author

Listed:
  • Shilpi Jain

    (Department of Mathematics, Poornima College of Engineering, Jaipur 302021, India)

  • Rahul Goyal

    (Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India)

  • Praveen Agarwal

    (Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
    Department of Mathematics, Harish-Chandra Research Institute, Allahabad 211019, India
    International Center for Basic and Applied Sciences, Jaipur 302029, India)

  • Juan L. G. Guirao

    (Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Murcia, Spain
    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

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.

Suggested Citation

  • Shilpi Jain & Rahul Goyal & Praveen Agarwal & Juan L. G. Guirao, 2021. "Some Inequalities of Extended Hypergeometric Functions," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2702-:d:663990
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