Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12 and X17

  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Rathie, Arjun K. (Department of Mathematics, School of Mathematical & Physical Sciences, Central University of Kerala, Riverside Transit Campus)
  • Received : 2012.11.17
  • Accepted : 2013.03.27
  • Published : 2014.12.23
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Abstract

In the theory of hypergeometric functions of one or several variables, a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at generalizing the following transformation formula for the Exton's triple hypergeometric series $X_{12}$ and $X_{17}$: $$(1+2z)^{-b}X_{17}\;\left(a,b,c_3;\;c_1,c_2,2c_3;\;x,{\frac{y}{1+2z}},{\frac{4z}{1+2z}}\right)\\{\hfill{53}}=X_{12}\;\left(a,b;\;c_1,c_2,c_3+{\frac{1}{2}};\;x,y,z^2\right).$$ The results are derived with the help of two general hypergeometric identities for the terminating $_2F_1(2)$ series which were very recently obtained by Kim et al. Four interesting results closely related to the Exton's transformation formula are also chosen, among ten, to be derived as special illustrative cases of our main findings. The results easily obtained in this paper are simple and (potentially) useful.

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References

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