Hypergeometric identities of Cayley and Orr types: Some alternative approaches

Recently, E. Montaldi and H. M. Srivastava [1] gave a rather simple proof of the classic hypergeometric identities of Cayley and Orr, which completely avoided the use both of differential equations and of relations between generalized hypergeometric series. The main object of this sequel to the earlier work [1] is to present a similar analysis of the various other hypergeometric identities of Cayley and Orr types. The alternative derivations given here provide a novel insight into the structure of these hypergeometric identities.