• 대한수학회논문집
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• 제19권3호
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• pp.569-576
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• 2004

In 1965, Bhatt and Pandey obtained the Watson's theorem for double series by using Dioxon's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty three results for double series closely related to the Watson's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty three summation formulas closely related to the Dison's theorem on the sum of a $_3F_2$ obtained in earlier work by Lavoie, Grondin, Rathie and Arora.

• 호남수학학술지
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• 제26권1호
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• pp.119-132
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• 2004

In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty five results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty five summation formulas closely related to the Watson's theorem on the sum of a $_3F_2$ obtained recently by Lavoie, Grondin, and Rathie.

• 호남수학학술지
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• 제35권4호
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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].

• 호남수학학술지
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• 제33권1호
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• pp.43-50
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• 2011

The aim of this paper is to obtain twenty five Eulerian type double integrals in the form of a general double integral involving Kamp$\'{e}$ de F$\'{e}$riet function. The results are derived with the help of the generalized classical Watson's theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.

• 대한수학회보
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• 제44권4호
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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.

• 충청수학회지
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• 제24권2호
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• pp.205-212
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• 2011

The aim of this paper is to obtain twenty five Eulerian type single integrals in the form of a general single integral involving $Kamp\acute{e}$ de $F\acute{e}riet$ function. The results are derived with the help of the generalized classical Watson's theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.

• 대한수학회논문집
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• 제14권1호
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• pp.217-222
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• 1999

The aim of this research is to provide a generalization of the well-known, interesting and useful identity due to Preece by using classical Dixon`s theorem on a sum of \ulcornerF\ulcorner.

• Kyungpook Mathematical Journal
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• 제16권2호
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• pp.215-217
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• 1976

• 대한수학회논문집
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• 제30권3호
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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.

• Journal of the Korean Statistical Society
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• 제30권1호
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• pp.21-30
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• 2001

Suppose we observe a set of data (X$_1$,Y$_1$(, …, (X$_{n}$,Y$_{n}$) and use the Nadaraya-Watson regression estimator to estimate m(x)=E(Y│X=x). in this article bandwidth selection problem for the Nadaraya-Watson regression estimator is investigated. In particular cross validation method based on average square error(ASE) is considered. Theoretical results here include a central limit theorem that quantifies convergence rates of the bandwidth selector.tor.