• 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.

• East Asian mathematical journal
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• v.16 no.1
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• pp.81-87
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• 2000

Bose and Mitra obtained certain interesting tansformations of the generalized hypergeometric series by using some known summation formulas and employing suitable contour integrations in complex function theory. The authors aim at providing another transformation of the generalized hypergeometric series by making use of the technique as those of Bose and Mitra and a known summation formula, which Bose and Mitra did not use, for the Gaussian hypergeometric series.

• East Asian mathematical journal
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• v.39 no.3
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• pp.299-303
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• 2023

The aim of this note is to provide three derivations of the well-known Gregory-Leibniz series for π via a hypergeometric series approach.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.707-714
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• 2000

The authors aim at presenting a presumably new transformation formula involving generalized hypergeometric series by making use of series rearrangement technique which is one of the most effective methods for obtaining generating functions or other identities associated with (especially) the hypergeometric series. They also consider a couple of interesting special cases of their main result.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.495-513
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• 2021

The hypergeometric series of four variables are introduced and studied by Bin-Saad and Younis recently. In this line, we derive several fractional derivative formulas, integral representations and operational formulas for new quadruple hypergeometric series.

• 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.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.677-684
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• 2014

In the theory of hypergeometric functions of one or several variables, a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at generalizing the following transformation formula for the Exton's triple hypergeometric series $X_{12}$ and $X_{17}$: $$(1+2z)^{-b}X_{17}\;\left(a,b,c_3;\;c_1,c_2,2c_3;\;x,{\frac{y}{1+2z}},{\frac{4z}{1+2z}}\right)\\{\hfill{53}}=X_{12}\;\left(a,b;\;c_1,c_2,c_3+{\frac{1}{2}};\;x,y,z^2\right).$$ The results are derived with the help of two general hypergeometric identities for the terminating $_2F_1(2)$ series which were very recently obtained by Kim et al. Four interesting results closely related to the Exton's transformation formula are also chosen, among ten, to be derived as special illustrative cases of our main findings. The results easily obtained in this paper are simple and (potentially) useful.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.187-189
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• 2008

We aim at presenting an interesting result for a reducibility of Exton's triple hypergeometric series $X_2$. The identity to be given here is obtained by combining Exton's Laplace integral representation for $X_2$ and Henrici's formula for the product of three hypergeometric series.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.911-925
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• 2016

We obtain q-derivatives of Srivastava's general triple q-hypergeometric series with respect to its parameters. The particular cases leading to results for three Srivastava's triple q-hypergeometric series $H_{A,q}$, $H_{B,q}$ and $H_{C,q}$ are also considered.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.11-16
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• 1997

In this paper we will study a p-adic analogue of Kummer's theorem[6],[7], which gives the value at x = -1 of a well-piosed $_2F_1$ hypergeometric series.