• Kyungpook Mathematical Journal
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• 제34권2호
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• pp.193-197
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• 1994

• 대한수학회논문집
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• 제15권4호
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• pp.691-696
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• 2000

Very recently Professor Exton derived an interesting hypergeometric generating relation. The authors aim at deriving another hypergeometric generating relation by using the same technique developed by Exton. Some interesting special cases have also been given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.255-259
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• 2006

In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a $_3F_2$ by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..

• 대한수학회논문집
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• 제14권3호
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• pp.641-647
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• 1999

The object of this note is to give sums of certain families of series which are initiated from their special cases considered here. Pelevant connections of the series identities presented here with those given elsewhere are also pointed out.

• 대한수학회논문집
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• 제29권1호
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• pp.65-74
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• 2014

The well known quadratic transformation formula due to Gauss: $$(1-x)^{-2a}{_2F_1}\[{{a,b;}\\\hfill{21}{2b;}}\;-\frac{4x}{(1-x)^2}\]={_2F_1}\[{{a,a-b+\frac{1}{2};}\\\hfill{65}{b+\frac{1}{2};}}\;x^2\]$$ plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for $_2F_1$. Our main objective of this paper is to deduce some interesting known or new results for the series $_2F_1(x)$ by using the above Gauss's quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.