• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.473-496
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• 2022

In 2014, Liu and Wang established a large number of interesting reduction, transformation and summation formulas for the Kampé de Fériet function. Inspired by the work, we aim to find further several transformation and reduction formulas for the Kampé de Fériet function. Theses formulas are mainly based on the formulas given by Liu and Wang [33].

• Honam Mathematical Journal
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• v.31 no.2
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• pp.167-176
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• 2009

The aim of this paper is to obtain three interesting results for reducibility of Kamp$\'{e}$ de $\'{e}$riet function. The results are derived with the help of contiguous Gauss's second summation formulas obtained earlier by Lavoie et al. The results obtained by Bailey, Rathie and Nagar follow special cases of our main findings.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.169-187
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• 2022

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+1F_p(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.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.569-576
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• 2004

In 1965, Bhatt and Pandey obtained the Watson's theorem for double series by using Dioxon's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty three results for double series closely related to the Watson's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty three summation formulas closely related to the Dison's theorem on the sum of a $_3F_2$ obtained in earlier work by Lavoie, Grondin, Rathie and Arora.