A note on certain classes of transformation formulas involving several variables (Q1281193)

The authors prove several multiple-series identities, all of which stem essentially from the elementary series identity [see, for example, \textit{H. M. Srivastava} and \textit{H. L. Manocha}, A treatise of generating functions (1984; Zbl 0535.33001), p. 101, Lemma 3(6)]: \[ \sum_{n=0}^\infty \sum_{k=0}^{[n/m]} \Omega(k,n)= \sum_{n=0}^\infty \sum_{k=0}^\infty \Omega(k,n+mk) \quad (m=1,2,3,\dots), \] where, as usual \([\lambda]\) denotes the largest integer in \(\lambda\). From these multiple-series identities, they derive many applications to multivariable hypergeometric functions, thereby relating their work to some of the results given earlier by \textit{H. M. Srivastava} [J. Phys. A 18, 3079-3085 (1985; Zbl 0556.33003); J. Aust. Math. Soc., Ser. A 43, 187-198 (1987; Zbl 0596.33006)], and by \textit{C. C. Grosjean} and \textit{H. M. Srivastava} [J. Comput. Appl. Math. 37, No. 1-3, 287-299 (1991; Zbl 0736.33009)].