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On Extended Beta Function and Related Inequalities

Author

Listed:
  • Rakesh K. Parmar

    (Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry 605014, India)

  • Tibor K. Pogány

    (Institute of Applied Mathematics, John von Neumann Faculty of Informatics, Óbuda University, 1034 Budapest, Hungary
    Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia)

  • Ljiljana Teofanov

    (Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia)

Abstract

In this article, we consider a unified generalized version of extended Euler’s Beta function’s integral form a involving Macdonald function in the kernel. Moreover, we establish functional upper and lower bounds for this extended Beta function. Here, we consider the most general case of the four-parameter Macdonald function K ν + 1 2 p t − λ + q ( 1 − t ) − μ when λ ≠ μ in the argument of the kernel. We prove related bounding inequalities, simultaneously complementing the recent results by Parmar and Pogány in which the extended Beta function case λ = μ is resolved. The main mathematical tools are integral representations and fixed-point iterations that are used for obtaining the stationary points of the argument of the Macdonald kernel function K ν + 1 2 .

Suggested Citation

  • Rakesh K. Parmar & Tibor K. Pogány & Ljiljana Teofanov, 2024. "On Extended Beta Function and Related Inequalities," Mathematics, MDPI, vol. 12(17), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2709-:d:1467988
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