대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권1호
  • /
  • Pages.65-74
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  • 2014
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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NEW RESULTS FOR THE SERIES 2F2(x) WITH AN APPLICATION

  • Choi, Junesang (Department of Mathematics Dongguk University) ;
  • Rathie, Arjun Kumar (Department of Mathematics School of Mathematical & Physical Sciences Central University of Kerala)
  • 투고 : 2013.04.29
  • 발행 : 2014.01.31
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초록

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.

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참고문헌

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피인용 문헌

  1. Generalized hypergeometric function identities at argument±1 vol.25, pp.11, 2014, https://doi.org/10.1080/10652469.2014.939078