• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.789-797
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• 2017

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and its associated alternating version whose terms contain a (p, q)-extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.5-12
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• 1998

We evaluate the sum of certain class of generalized hypergeometric series of unit argument. Summation formulas, contiguous to Watson's, Whipple's, Lavoie's and Choi's theorems in the theory of the generalized hypergeometric series, are obtained. Certain limiting cases of these results are given.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.473-482
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeo-metric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_C$.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.3
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• pp.149-153
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• 2023

The aim of this note is to derive two known combinatorial identities via a hypergeometric series approach using Saalschiitz's classical summation theorem.

• 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.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1239-1248
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• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.603-608
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• 2005

In 1999 and 2003, Padmanabham established two results (one each) for Exton's triple hypergeometric series $X_8$. We aim at showing that Exton's later result can be derived from his former one.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.61-71
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• 2010

The aim of this paper is to extend a number of transformation formulas for the four $X_4$, $X_5$, $X_7$, and $X_8$ among twenty triple hypergeometric series $X_1$ to $X_{20}$ introduced earlier by Exton. The results are derived from the generalized Kummer's theorem and Dixon's theorem obtained earlier by Lavoie et al..

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.743-751
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• 2007

The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.517-521
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• 2009

The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$ by using a different method from that of Padmanabham's. An interesting special case is also pointed out.