Junesang Choi and Arjun K. Rathie Dongguk University, Central University of Kerala
Abstract : A large number of summation and transformation formulas involving (generalized) hypergeometric functions have been developed by many authors. Here we aim at establishing two (presumably) new general hypergeometric transformations. The results are derived by manipulating the involved series in an elementary way with the aid of certain hypergeometric summation theorems obtained earlier by Rakha and Rathie. Relevant connections of certain special cases of our main results with several known identities are also pointed out.
Keywords : gamma function, hypergeometric function, generalized hypergeometric function, Kamp\'e de F\'eriet function, Kummer's second summation theorem, Dixon and Whipple's summation theorems