• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.419-427
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• 2011

In this paper, making use of transformation due to S. N. Singh [21], an at-tempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.885-898
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• 2017

The Bailey lemma has been a powerful tool in the discovery of identities of Rogers-Ramanujan type and also ordinary and basic hyper-geometric series identities. The mechanism of Bailey lemma has also led to the concepts of Bailey pair and Bailey chain. In the present work certain new WP-Bailey pairs have been established. We also have deduced a number of basic hypergeometric series identities as an application of new WP-Bailey pairs.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.207-236
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• 2018

We obtain recursion formulas for q-hypergeometric and q-Appell series. We also find recursion formulas for the general double q-hypergeometric series. It is shown that these recursion relations can be expressed in terms of q-derivatives of the respective q-hypergeometric series.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.395-403
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• 2005

The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series $series\;_2{\phi}_1$ corresponding to Gauss's contiguous relations for the hypergeometric series $series\;_2F_1$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known q-analogue of Kummer's theorem.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.521-533
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• 2020

In this paper, we compute the Bergman kernel for Ω_p,q,r = {(z, z', w) ∈ ℂ² × Δ : |z|^2p < (1 - |z'|^2q)(1 - |w|²)^r}, where p, q, r > 0 in terms of multivariable hypergeometric series. As a consequence, we obtain the behavior of K_Ωp,q,r (z, 0, 0; z, 0, 0) when (z, 0, 0) approaches to the boundary of Ω_p,q,r.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.131-143
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• 2005

We give bibasic expansion for basic Appell functions ${\Phi}^{(1)}$ and ${\Phi}^{(2)}$, and their integral representations. We also give a continued fraction representation for ${\Phi}^{(2)}$.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.495-505
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• 2018

The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.341-345
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• 2007

In this paper we show that the second order mock theta function, given by Hikami, is bounded and satisfies the second condition for the mock theta functions.