Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON GENERALIZED EXTENDED BETA AND HYPERGEOMETRIC FUNCTIONS

  • Shoukat Ali (Department of Mathematics, Government Engineering College Bikaner) ;
  • Naresh Kumar Regar (Department of Mathematics, Government Engineering College Bikaner) ;
  • Subrat Parida (Department of Mathematics, Ramanujan School of Mathematical Sciences, Pondicherry University-A Central University)
  • Received : 2023.12.03
  • Accepted : 2024.01.13
  • Published : 2024.06.25
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Abstract

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

Keywords

Acknowledgement

Authors are thankful to the reviewers for giving valuable suggestions to improve the paper in the present form.

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