Some families of generating functions for a certain class of three-variable polynomials

Abstract

The present investigation is a continuation of the works initiated by Srivastava [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), pp. 1–6] and followed by several papers such as (among others) [A. Altın, E. Erkuş, and M.A. Özarslan, Families of linear generating functions for polynomials in two variables, Integral Transforms Spec. Funct. 17 (2006), pp. 315–320; B. González, J. Matera, and H.M. Srivastava, Some q-generating functions and associated generalized hypergeometric polynomials, Math. Comput. Modelling 34 (2001), pp. 133–175; S.-D. Lin, Y.-S. Chao, and H.M. Srivastava, Some families of hypergeometric polynomials and associated integral representations, J. Math. Anal. Appl. 294 (2004), pp. 399–411; S.-D. Lin, H.M. Srivastava, and P.-Y. Wang, Some families of hypergeometric transformations and generating relations, Math. Comput. Modelling 36 (2002), pp. 445–459; E. Özergin, M.A. Özarslan, and H.M. Srivastava, Some families of generating functions for a class of bivariate polynomials, Math. Comput. Modelling 50 (2009), pp. 1113–1120]. In this study, we introduce a family of three-variable polynomials and derive a number of two-sided linear generating functions between these polynomials and another family of two-variable polynomials. Furthermore, mixed multilateral and multilinear generating functions are derived for these polynomials. Several other results of the above-mentioned types are also considered.