Generalization of a quadratic transformation due to Exton

Abstract

Exton [Ganita 54(2003)13-15] obtained numerous new quadratic transformations involving hypergeometric functions of order two and of higher order by applying various known classical summation theorems to a general transformation formula based on the Bailey transformation. We obtain the generalization of one of the Exton quadratic transformations. The results are derived with the help of a generalization of Dixon's summation theorem for the series ${}_3F_2$ obtained earlier by Lavoie {\em et al}. Several interesting known as well as new special cases and limiting cases are also given.