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Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function

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
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates)

  • Antonella Lupica

    (Department of Economics, Engineering, Society and Business Organization-DEIM Department, Tuscia University, 01100 Viterbo, Italy)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, 00186 Roma, Italy)

Abstract

The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.

Suggested Citation

  • Shilpi Jain & Rahul Goyal & Praveen Agarwal & Antonella Lupica & Clemente Cesarano, 2021. "Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function," Mathematics, MDPI, vol. 9(22), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2944-:d:682072
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