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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

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.

키워드

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