Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions

  • Abbas Kareem Wanas Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
  • Najah Ali Jiben Al-Ziadi Department of Mathematics, College of Education, University of Al-Qadisiyah, Iraq
Keywords: holomorphic function, beta negative binomial distribution, probability, coefficient estimates, integral representation, neighborhood, subordination


The purpose of this article is to derive the necessary and sufficient conditions for the power series 〖P℘〗_(ℷ,γ)^μ (t) whose coefficients are probabilities of the beta negative binomial distribution to be in the family F(σ,τ,ϵ,η,μ,ℷ,γ) of holomorphic functions which are defined in the open unit disk. We establish a number of important geometric properties, such as, coefficient estimates, extreme points, neighborhood property, integral representation, radii of starlikeness and convexity and Hadamard product properties for functions belongs to this family. Also we determinate some differential subordination properties of the power series 〖P℘〗_(ℷ,γ)^μ (t).


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How to Cite
Wanas, A. K., & Al-Ziadi, N. A. J. (2021). Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions. Earthline Journal of Mathematical Sciences, 6(2), 271-292.