• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.519-526
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• 2014

A large number of summation and transformation formulas involving (generalized) hypergeometric functions have been developed by many authors. Here we aim at establishing two (presumably) new general hypergeometric transformations. The results are derived by manipulating the involved series in an elementary way with the aid of certain hypergeometric summation theorems obtained earlier by Rakha and Rathie. Relevant connections of certain special cases of our main results with several known identities are also pointed out.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.73-82
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• 2017

In this paper we aim to demonstrate how one can obtain so far unknown Laplace transforms for the generalized hypergeometric functions $_pF_p$ for p = 2, 3, 4, and 5 by employing known summation theorems available in the literature.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.701-706
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• 2013

Summation theorems for hypergeometric series $_2F_1$ and generalized hypergeometric series $_pF_q$ play important roles in themselves and their diverse applications. Some summation theorems for $_2F_1$ and $_pF_q$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $_3F_2$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].

• 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.46 no.6
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• pp.1061-1068
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• 2009

The intimate relation between the 3-j coefficient in Quantum Theory of Angular Momentum (QTAM) and the $_3F_2(1)$ hypergeometric series is exploited to derive new summation theorems, from formulas for the 3-j coefficient.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.979-990
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• 2017

Inspired by the results obtained by Brychkov ([2]), the authors evaluate a large number of new and interesting double definite integrals. The results are obtained with the use of classical hypergeometric summation theorems and a well-known double finite integral due to Edwards ([3]). The results are given in terms of Psi and Hurwitz zeta functions suitable for numerical computations.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.227-237
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• 2015

By employing certain extended classical summation theorems, several surprising ${\pi}$ and other formulae are displayed.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.865-874
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• 2017

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems have been found interesting applications in obtaining various series identities for ${\Pi}$, ${\Pi}^2$ and ${\frac{1}{\Pi}}$. The aim of this research paper is to provide twelve general formulas for ${\frac{1}{\Pi}}$. On specializing the parameters, a large number of very interesting series identities for ${\frac{1}{\Pi}}$ not previously appeared in the literature have been obtained. Also, several other results for multiples of ${\Pi}$, ${\Pi}^2$, ${\frac{1}{{\Pi}^2}}$, ${\frac{1}{{\Pi}^3}}$ and ${\frac{1}{\sqrt{\Pi}}}$ have been obtained. The results are established with the help of the extensions of classical Gauss's summation theorem available in the literature.

• East Asian mathematical journal
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• v.22 no.1
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• pp.71-77
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• 2006

By applying various known summation theorems to a general transformation formula based upon Bailey's transformation theorem due to Slater, Exton has obtained numerous and new quadratic transformations involving hypergeometric functions of order greater than two(some of which have typographical errors). We aim at first deriving a general quadratic transformation formula due to Exton and next providing a list of quadratic formulas(including the corrected forms of Exton's results) and some more results.

• 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.