• 호남수학학술지
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• 제32권1호
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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..

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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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.

• 대한수학회보
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• 제49권3호
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• pp.621-633
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• 2012

By establishing a new summation formula for the series $_3F_2(\frac{1}{2})$, recently Rathie and Pogany have obtained an interesting result known as Kummer type II transformation for the generalized hypergeometric function $_2F_2$. Here we aim at deriving their result by using a very elementary method and presenting two elegant results for certain terminating series $_3F_2(2)$. Furthermore two interesting applications of our new results are demonstrated.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.293-299
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• 2019

A number of identities associated with the product of generalized hypergeometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series $_2F_2$. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones.

• 호남수학학술지
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• 제37권2호
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• pp.245-252
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• 2015

This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function $_2F_2(x)$ by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series $_3F_2$ obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.

• East Asian mathematical journal
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• 제17권2호
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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.

• 호남수학학술지
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• 제37권3호
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• pp.339-352
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• 2015

We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.

• 호남수학학술지
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• 제31권2호
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• pp.167-176
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• 2009

The aim of this paper is to obtain three interesting results for reducibility of Kamp$\'{e}$ de $\'{e}$riet function. The results are derived with the help of contiguous Gauss's second summation formulas obtained earlier by Lavoie et al. The results obtained by Bailey, Rathie and Nagar follow special cases of our main findings.

• 호남수학학술지
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• 제36권2호
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• pp.345-355
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• 2014

The main objective of this paper is to obtain a formula containing eleven interesting results for the reducibility of Kamp$\acute{e}$ de F$\acute{e}$riet function. The results are derived with the help of two general results for the series $_2F_1(2)$ very recently presented by Kim et al. Well known Kummer's second theorem and its contiguous results proved earlier by Rathie and Nagar, and Kim et al. follow special cases of our main findings.

• 대한수학회논문집
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• 제27권1호
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• pp.129-135
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• 2012

The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_3F_2$(1) and $_4F_3(1)$ already available in the literature.