q -Difference equations for generalized homogeneous q -operators and certain generating functions.

In this paper, we give two generalized homogeneousq-operator identities, which are obtained byq-difference equations. In addition, we generalize certain generating functions from Chen et al. [W.Y.C. Chen, A. M. Fu, and B. Zhang,The homogeneousq-difference operator, Adv. Appl. Math. 31 (2003), pp. 659–668] and Saad and Sukhi [H. L. Saad and A.A. Sukhi,Another homogeneousq-difference operator, Appl. Math. Comput. 215 (2010), pp. 4332–4339] by the method ofq-difference equations. Moreover, we gainU(n+1) generalizations of generating functions for Verma–Jain polynomials byq-difference equations. Finally, we obtain two transformational identities byq-difference equations. [ABSTRACT FROM AUTHOR]