Some results involving series representations of hypergeometric functions

In this paper, we prove some generalisations of several theorems given in [K.A. Driver, S.J. Johnston, An integral representation of some hypergeometric functions, Electron. Trans. Numer. Anal. 25 (2006) 115–120] and examine some special cases which correspond to a transformation given by Chaundy in [T.W. Chaundy, An extension of hypergeometric functions, I., Quart. J. Maths. Oxford Ser. 14 (1943) 55–78] and other transformations involving the Riemann zeta function and the beta function.