Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications

It is well known that classical summation theorems such as of Gauss, Gauss second, Kummer and Bailey for the series 2 F 1 and Watson, Dixon and Whipple for the series 3 F 2 play an important role in the theory of hypergeometric and generalized hypergeometric series. Applications of these summation theorems are well known. The aim of this research paper is to provide the generalizations of the above-mentioned classical summation theorems in the most general case.