A new proof of classical Dixon's summation theorem for the series ${}_{3}F_{2}(1)$

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems such as those of Gauss, Gauss second, Kummer and Bailey for the series 2F1; Watson, Dixon, Whipple and Saalschütz play a key role. Applications of the above mentioned theorems are well known now. For very interesting applications of these theorems, we refer a paper by Bailey [1]. Here we shall mention the following summation theorems that will be required in our present investigation. Gauss summation theorem: [2,3,4]