Applications of some theorems of Carlitz and Srivastava (Q1058025)

The author applies a theorem due to the reviewer [Indagationes Math. 42, 221-234, 234-246 (1980; Zbl 0415.33008); see p. 224, theorem 2] in order to derive a multivariable generating function for the polynomials \(P_ n^{(\alpha,\beta)}(x,y;a,k)\) studied by \textit{I. K. Khanna} and \textit{P. Pandey} [Indian J. Pure Appl. Math. 13, 1075-1084 (1982; Zbl 0502.33009)]. He also applies a theorem of \textit{L. Carlitz} [SIAM J. Math. Anal. 8, 518-532 (1977; Zbl 0357.33004)] to these polynomials. For a systematic presentation of results of the types discussed in this paper, see Chapters 7 and 8 of the latest work on the subject by the reviewer and \textit{H. L. Manocha} [A treatise on generating functions (1984; Zbl 0535.33001)].