Some multiple-series extensions of the multivariable generating functions of Srivastava (Q1058026)

The authors prove some interesting multiple-series extensions of several results on generating functions, which were given earlier by \textit{H. M. Srivastava} and the reviewer [J. Reine Angew. Math. 283/284, 265-274 (1976; Zbl 0315.33003)], and \textit{H. M. Srivastava} [Z. Angew. Math. Mech. 57, 339-340 (1977; Zbl 0342.33009); Indagationes Math. 43, 129-138 (1981; Zbl 0437.33008)]. Their proofs run parallel to those used by these earlier authors. For a systematic presentation of such classes of multilinear generating functions, see Chapter 9 on the latest work on the subject by \textit{H. M. Srivastava} and \textit{H. L. Manocha} [A treatise on generating functions (1984; Zbl 0535.33001)].