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http://dx.doi.org/10.22771/nfaa.2022.27.01.11

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))
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.1, 2022 , pp. 169-187 More about this Journal
Abstract
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.
Keywords
Hypergeometric functions; generalized hypergeometric functions; summation formulas for $_pF_q$; transformation formulas for $_pF_q$; Kampe de Feriet series; Faa di Bruno's formula; Bell polynomials;
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