Partial sums of analytic functions defined by binomialdistribution and negative binomial distribution

Rubab Nawaz, Saira Zainab, Fairouz Tchier, Qin Xin, Afis Saliu, Sarfraz Nawaz Malik

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Abstract

The study of statistical distributions in a complex variable is one of
the most vibrant areas of research. The complex analogue of many
distributions has been studied. This article introduces the complex
analogue of Binomial distribution and Negative Binomial distribution and studies certain geometrical properties of these analogues.
It comprises the study of analytic functions defined by using the
complex versions of Binomial distribution and Negative Binomial distribution functions. It includes the problems of finding the lower
bounds of real parts of certain ratios of partial sums to the infinite
series sums for these analytic functions. Such lower bounds are determined for the said analytic functions, for their first derivatives and for
the Alexander transformation of these analytic functions.
Original languageEnglish
Article number2022.2109630
Pages (from-to)554-572
Number of pages20
JournalApplied Mathematics in Science and Engineering
Volume30
Issue number1
Publication statusPublished - 9 Aug 2022

Keywords

  • Analytic functions
  • statistical distribution
  • binomial distribution
  • partial sums
  • ; negative binomial distributions

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