Extension of a quadratic transformation due to Exton

Keywords: Quadratic transformation Hypergeometric function of order two Kummer–type transformations Bailey's transform a b s t r a c t By applying various known summation theorems to a general formula based upon Bailey's transform theorem due to Slater, Exton has obtained numerous new quadratic transformations involving hypergeometric functions of two and of higher order. Some of the results have typographical errors and have been corrected recently by Choi and Rathie. In addition, two new quadratic transformation formul were also obtained [Junesang Choi, A.K. Rathie, Quadratic transformations involving hypergeometric functions of two and higher order, EAMJ, East Asian Math. J. 22 (2006) 71–77]. The aim of this research paper is to obtain a generalization of one of the Exton's quadratic transformation. The results are derived with the help of generalized Kummer's theorem obtained earlier by Lavoie, Grondin and Rathie. As special cases, we mention six interesting results closely related to that of Exton's result. As a consequence of Bailey's transform, Slater [2, Eq. (2.4.10), p. 60] gave a useful and general hypergeometric transform. However, in our present investigations, we are interested in the following special case: