Nonlinear Functional Analysis and Applications

  • 제27권1호
  • /
  • Pages.169-187
  • /
  • 2022
  • /
  • 1229-1595(pISSN)
  • /
  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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A POWER SERIES ASSOCIATED WITH THE GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE UNIT ARGUMENT WHICH ARE INVOLVED IN BELL POLYNOMIALS

  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Qureshi, Mohd Idris (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (A Central University)) ;
  • Majid, Javid (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (A Central University)) ;
  • Ara, Jahan (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (A Central University))
  • 투고 : 2021.07.26
  • 심사 : 2021.12.05
  • 발행 : 2022.03.15
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초록

There have been provided a surprisingly large number of summation formulae for generalized hypergeometric functions and series incorporating a variety of elementary and special functions in their various combinations. In this paper, we aim to consider certain generalized hypergeometric function 3F2 with particular arguments, through which a number of summation formulas for p+1Fp(1) are provided. We then establish a power series whose coefficients are involved in generalized hypergeometric functions with unit argument. Also, we demonstrate that the generalized hypergeometric functions with unit argument mentioned before may be expressed in terms of Bell polynomials. Further, we explore several special instances of our primary identities, among numerous others, and raise a problem that naturally emerges throughout the course of this investigation.

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과제정보

The authors would like to express their deep-felt thanks for the reviewers' encouraging comments. The first-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R111A1A01052440).

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