Alternative Derivations of Certain Summation Formulas Contiguous to Dixon's Summation Theorem for a Hypergeometric 3F2 Series

Abstract

In 194, Lavoie et al. have obtained twenty tre interesting resultsclosely related to the clasical Dixon’s theorem on the sum of a 3F2 by making asystematic use of some known relations among contiguous functions. We aim atshowing that hese results can be derived by using the same te chnique developedby Bailey with the help of Gaus’s umation theorem and gene ralized Kumer’stheorem obtained by Lavoie et al..