• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.385-389
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• 2010

In 1997, Exton, by mainly employing a widely-used process of resolving hypergeometric series into odd and even parts, obtained some new and interesting summation formulas with arguments 1 and -1. We aim at showing how easily many summation formulas can be obtained by simply combining some known summation formulas. Indeed, we present 22 results in the form of two generalized summation formulas for the generalized hypergeometric series $_4F_3$, including two Exton's summation formulas for $_4F_3$ as special cases.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.469-475
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• 2005

The authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan. The results are derived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.35-44
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• 2012

Motivated by the extension of classical Dixon's summation theorem for the series $_3F_2$ given by Lavoie, Grondin, Rathie and Arora, the authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan.

• 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].

• East Asian mathematical journal
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• v.33 no.5
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• pp.527-531
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• 2017

We aim to prove a known summation formula for the series $_4F_3(1)$ by mainly using a similar method as in [2], which is different from that in [3]. The method of proof here as well as that in [2] is potentially useful in getting some other summation formulas for $_pF_q$.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.527-534
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• 2013

We first aim at proving an interesting easily derivable summation formula. Then it is easily seen that this formula immediately yields a hypergeometric summation theorem recently added to the literature by Qureshi et al. Moreover we apply the main formulas to present some interesting summation formulas, whose special cases are also seen to yield the earlier known results.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.293-301
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• 2022

The present paper concerns with a study of certain generating functions and summation formulas of generalized Poisson-Charlier polynomials. Some special cases are also discussed.

• East Asian mathematical journal
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• v.17 no.2
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• pp.233-237
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• 2001

The authors aim at presenting summation formulas of Appell's function $F_1$: $$F_1(a;b,b';1+a+b-b'+i;1,-1)\;(i=0,\;{\pm}1,\;{\pm}2,\;{\pm}3,\;{\pm}4,\;{\pm}5)$$, which, for i=0, yields a known result due to Srivastava.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.223-228
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• 2005

In 2001, Choi, Harsh & Rathie [Some summation formulas for the Appell's function $F_1$. East Asian Math. J. 17 (2001), 233-237] have obtained 11 results for the Appell's function $F_1$ with the help of Gauss's summation theorem and generalized Kummer's summation theorem. We aim at presenting 22 more results for $F_1$ with the help of the generalized Gauss's second summation theorem and generalized Bailey's theorem obtained by Lavoie, Grondin & Rathie [Generalizations of Whipple's theorem on the sum of a $_3F_2$. J. Comput. Appl. Math. 72 (1996), 293-300]. Two interesting (presumably) new special cases of our results for $F_1$ are also explicitly pointed out.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.185-191
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• 2010

Srivastava noticed the existence of three additional complete triple hypergeometric functions $H_A$, $H_B$ and $H_C$ of the second order in the course of an extensive investigation of Lauricella's fourteen hypergeometric functions of three variables. In 2004, Rathie and Kim obtained four summation formulas containing a large number of very interesting reducible cases of Srivastava's triple hypergeometric series $H_A$ and $H_C$. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava's $H_C$ with the help of generalized Dixon's theorem and generalized Whipple's theorem on the sum of a $_3F_2$ obtained earlier by Lavoie et al.. Some special cases of our results are also considered.